{ "cells": [ { "cell_type": "markdown", "id": "31fe6c1c", "metadata": {}, "source": [ "# 11 · Mass Springs: from Hooke's Law to a Sagging Cable\n", "\n", "The spring is the simplest elastic element: two point masses joined by one edge. We derive\n", "Hooke's law from the spring energy, give the spring a mass and compare Forward Euler, Backward\n", "Euler and BDF2 in *phase space*, then chain many springs into a cable and let it sag under\n", "gravity, once by minimizing its energy and once by stepping it through time." ] }, { "cell_type": "markdown", "id": "d6dbbea7", "metadata": {}, "source": [ "Imports, and every tunable parameter of this notebook." ] }, { "cell_type": "code", "execution_count": 1, "id": "1d8db00a", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:31.586536Z", "iopub.status.busy": "2026-09-24T03:44:31.586460Z", "iopub.status.idle": "2026-09-24T03:44:32.145896Z", "shell.execute_reply": "2026-09-24T03:44:32.145320Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import os\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "import simkit\n", "from simkit.solvers import newton_solver\n", "import utils\n", "\n", "NOTEBOOK = \"011_mass_springs\" # this file's name\n", "RESULTS_DIR = utils.notebook_results_path(NOTEBOOK) # results/011_mass_springs/\n", "MEDIA_DIR = \"media\" # tracked copies for the website\n", "\n", "# 1 · single spring (node 0 is a fixed anchor, node 1 a free mass)\n", "SPRING_L0 = 1.0 # rest length l0\n", "K_SPRING = 1.0 # spring stiffness k (simkit's `ym`)\n", "CURVE_L_RANGE = (0.02, 2.0) # spring lengths for the energy / force curves\n", "N_CURVE = 200 # samples along those curves\n", "SWEEP_L_RANGE = (0.1, 1.9) # collapse / stretch range of the animation\n", "N_SWEEP = 45 # animation frames each way\n", "FPS = 20 # frame rate of the spring videos and the comparison video\n", "\n", "# 2 · oscillator\n", "MASS = 1.0 # mass of the free node\n", "U0 = 0.3 # initial stretch u = l - l0, released from rest\n", "DT_OSC = 0.1 # coarse time step, so the schemes visibly differ\n", "N_PERIODS = 3 # simulated oscillation periods\n", "OSC_FRAMES = 90 # frames in the oscillator video\n", "SCHEMES = [\"Forward Euler\", \"Backward Euler\", \"BDF2\"]\n", "\n", "# 3 · cable\n", "N_NODES = 21 # masses along the cable\n", "CABLE_LENGTH = 4.0 # rest length of the whole cable\n", "K_CABLE = 400.0 # stiffness k of every cable spring\n", "RHO = 1.0 # mass per unit rest length\n", "GRAVITY = -9.8 # vertical acceleration\n", "K_PIN = 1e5 # soft-pin penalty stiffness at both ends\n", "NEWTON_TOL = 1e-9 # step-size tolerance of the static Newton solve\n", "NEWTON_MAX_ITERS = 50 # iteration cap of the static Newton solve\n", "DT = 0.04 # time step of the dynamic run\n", "N_STEPS = 250 # Backward-Euler steps\n", "STEP_ITERS = 20 # Newton iterations per time step\n", "STEP_TOL = 1e-6 # step-size tolerance of each time step's Newton solve\n", "MONOTONE_TOL = 1e-6 # round-off allowance of the \"total energy never increases\" check\n", "CABLE_FPS = 40 # frame rate of the dynamic cable video (one frame per step)\n", "NEWTON_FPS = 2 # frame rate of the Newton-iterate video\n", "COMPARE_FRAMES = 80 # frames in the static-vs-dynamic comparison video\n", "FD_STEP = 1e-5 # central-difference step of the gradient check\n", "FD_NOISE = 0.1 # size of the random state used by the gradient check\n", "SEED = 0 # random seed of that state\n", "K_SWEEP = [100.0, 400.0, 1600.0] # spring stiffnesses of the parameter study\n", "CABLE_LIMS = ((-0.5, 4.5), (-2.6, 0.5)) # plot window of every cable figure" ] }, { "cell_type": "markdown", "id": "d9cd59f9", "metadata": {}, "source": [ "The notebook's two spring networks, drawn at rest (blue squares are pinned): a single spring\n", "whose node 0 is a fixed anchor (sections 1 and 2), and a cable of `N_NODES` masses pinned at both\n", "ends (section 3)." ] }, { "cell_type": "code", "execution_count": 2, "id": "61cdc04d", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:32.147956Z", "iopub.status.busy": "2026-09-24T03:44:32.147757Z", "iopub.status.idle": "2026-09-24T03:44:32.259323Z", "shell.execute_reply": "2026-09-24T03:44:32.258948Z" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X_spring = np.array([[0.0, 0.0], [SPRING_L0, 0.0]]) # node 0: anchor, node 1: free mass\n", "E_spring = np.array([[0, 1]])\n", "anchor = X_spring[:1]\n", "\n", "X = np.column_stack([np.linspace(0.0, CABLE_LENGTH, N_NODES), np.zeros(N_NODES)])\n", "E = np.column_stack([np.arange(N_NODES - 1), np.arange(1, N_NODES)]) # spring e joins nodes e, e+1\n", "pin_idx = np.array([0, N_NODES - 1])\n", "n, dim = X.shape\n", "\n", "fig, (ax_s, ax_c) = plt.subplots(1, 2, figsize=(12, 2.4), gridspec_kw={\"width_ratios\": [1, 2.4]})\n", "utils.plot_spring_network(ax_s, X_spring, E_spring, pins=[0], node_size=50, lw=3,\n", " title=\"single spring\", lims=((-0.25, 1.35), (-0.3, 0.3)))\n", "utils.plot_spring_network(ax_c, X, E, pins=pin_idx, node_size=50, lw=3,\n", " title=f\"cable: {N_NODES} masses, {len(E)} springs\",\n", " lims=((-0.25, CABLE_LENGTH + 0.25), (-0.3, 0.3)))\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"meshes.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"011_meshes.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cfbc8362", "metadata": {}, "source": [ "## 1 · The elastic energy of a single spring (Hooke's law)\n", "\n", "A spring stores energy through its edge vector $d = x_j - x_i$ (blind to translation), its length\n", "$l = \\lVert d\\rVert$ (blind to rotation) and its stretch $l - l_0$. Differentiating the quadratic\n", "energy gives the force, linear in the stretch and pointing back to rest: Hooke's law is derived,\n", "not assumed.\n", "\n", "$$\n", "\\psi = \\tfrac12\\,k\\,(l-l_0)^2, \\qquad f = -\\frac{d\\psi}{dl} = -k\\,(l-l_0).\n", "$$" ] }, { "cell_type": "markdown", "id": "0283dafb", "metadata": {}, "source": [ "`anchored_spring_system` turns that one spring into a mechanical system in the free mass's\n", "position $x \\in \\mathbb{R}^2$; the anchor is not a degree of freedom. It builds $\\psi$ and its\n", "derivatives from simkit's per-edge `mass_springs_*_element_d`, whose `ym` is the stiffness $k$\n", "itself (no rest-length normalization). Sections 1 and 2 hand its three functions to plots,\n", "integrators and Newton." ] }, { "cell_type": "code", "execution_count": 3, "id": "fa10e48c", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:32.260607Z", "iopub.status.busy": "2026-09-24T03:44:32.260540Z", "iopub.status.idle": "2026-09-24T03:44:32.262817Z", "shell.execute_reply": "2026-09-24T03:44:32.262544Z" } }, "outputs": [], "source": [ "def anchored_spring_system(anchor, k, l0):\n", " \"\"\"One spring from a fixed `anchor` to a free mass at x (2 DOFs): psi = 1/2 k (|x - anchor| - l0)^2.\"\"\"\n", " ym = np.array([[k]])\n", " rest_length = np.array([[l0]])\n", "\n", " def energy_func(x):\n", " d = x.reshape(1, 2) - anchor # edge vector\n", " E_spring = simkit.energies.mass_springs_energy_element_d(d, ym, rest_length).item()\n", " E_total = E_spring\n", " return E_total\n", "\n", " def gradient_func(x):\n", " d = x.reshape(1, 2) - anchor\n", " g_spring = simkit.energies.mass_springs_gradient_element_d(d, ym, rest_length).reshape(-1, 1)\n", " g_total = g_spring\n", " return g_total\n", "\n", " def hessian_func(x):\n", " d = x.reshape(1, 2) - anchor\n", " H_spring = simkit.energies.mass_springs_hessian_element_d(d, ym, rest_length)[0]\n", " H_total = H_spring\n", " return H_total\n", "\n", " return energy_func, gradient_func, hessian_func" ] }, { "cell_type": "markdown", "id": "f1ca6344", "metadata": {}, "source": [ "Slide the free mass along the axis from nearly collapsed to twice the rest length, reading the\n", "energy from `energy_func` and the force from `-gradient_func`. The printed deviations from the\n", "closed forms above are round-off; the plots show a parabola about $l_0$ and a straight force line\n", "crossing zero at $l_0$." ] }, { "cell_type": "code", "execution_count": 4, "id": "bbcb61ec", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:32.264192Z", "iopub.status.busy": "2026-09-24T03:44:32.264095Z", "iopub.status.idle": "2026-09-24T03:44:32.438176Z", "shell.execute_reply": "2026-09-24T03:44:32.437620Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |psi - k(l-l0)^2/2| = 0.0e+00, max |f + k(l-l0)| = 1.1e-16\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "energy_func, gradient_func, hessian_func = anchored_spring_system(anchor, K_SPRING, SPRING_L0)\n", "\n", "lengths = np.linspace(*CURVE_L_RANGE, N_CURVE)\n", "psi, force = [], []\n", "for l in lengths:\n", " x = np.array([[l], [0.0]])\n", " psi.append(energy_func(x))\n", " force.append(-gradient_func(x)[0, 0]) # axial force on the free mass\n", "psi, force = np.array(psi), np.array(force)\n", "print(f\"max |psi - k(l-l0)^2/2| = {np.abs(psi - 0.5 * K_SPRING * (lengths - SPRING_L0) ** 2).max():.1e}, \"\n", " f\"max |f + k(l-l0)| = {np.abs(force + K_SPRING * (lengths - SPRING_L0)).max():.1e}\")\n", "\n", "fig, (ax_e, ax_f) = plt.subplots(1, 2, figsize=(11, 4.5))\n", "ax_e.plot(lengths, psi, color=utils.SPRING_EDGE, lw=2.5)\n", "ax_e.axvline(SPRING_L0, color=\"0.6\", ls=\"--\", lw=1.5)\n", "ax_e.set_xlabel(\"spring length $l$\")\n", "ax_e.set_ylabel(r\"energy $\\psi=\\frac{1}{2}k(l-l_0)^2$\")\n", "ax_e.set_title(\"Energy is a parabola about the rest length\")\n", "ax_e.grid(True, color=\"0.92\")\n", "ax_f.plot(lengths, force, color=utils.SPRING_NODE, lw=2.5)\n", "ax_f.axhline(0, color=\"0.6\", lw=1.0)\n", "ax_f.axvline(SPRING_L0, color=\"0.6\", ls=\"--\", lw=1.5)\n", "ax_f.set_xlabel(\"spring length $l$\")\n", "ax_f.set_ylabel(r\"restoring force $f=-k(l-l_0)$\")\n", "ax_f.set_title(\"Force is linear in stretch (Hooke's law)\")\n", "ax_f.grid(True, color=\"0.92\")\n", "fig.suptitle(\"Collapsing / stretching a single spring\", y=1.02)\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"hooke.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"011_hooke.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "6a243481", "metadata": {}, "source": [ "Now collapse and re-stretch the spring while tracing its energy in lock-step, so the quadratic\n", "well around $l_0$ is unmistakable (the gray dashes are the rest shape)." ] }, { "cell_type": "code", "execution_count": 5, "id": "b61a5264", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:32.439388Z", "iopub.status.busy": "2026-09-24T03:44:32.439277Z", "iopub.status.idle": "2026-09-24T03:44:34.995264Z", "shell.execute_reply": "2026-09-24T03:44:34.994895Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sweep = np.concatenate([np.linspace(*SWEEP_L_RANGE, N_SWEEP), np.linspace(*SWEEP_L_RANGE[::-1], N_SWEEP)])\n", "states, psi_sweep = [], []\n", "for l in sweep:\n", " x = np.array([[l], [0.0]])\n", " states.append(np.vstack([anchor, x.T]))\n", " psi_sweep.append(energy_func(x))\n", "\n", "fig, anim = utils.animate_springs_energy(\n", " states, E_spring, sweep, {\"elastic\": psi_sweep}, rest=X_spring, lims=((-0.4, 2.2), (-0.8, 0.8)),\n", " xlabel=\"spring length $l$\", ylabel=\"elastic energy\", scene_title=\"spring (gray = rest)\",\n", " title=\"energy vs length\", colors={\"elastic\": utils.SPRING_EDGE}, pin_pts=anchor)\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"spring_collapse.mp4\"), fps=FPS,\n", " copy_to=os.path.join(MEDIA_DIR, \"011_spring_collapse.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "095c0714", "metadata": {}, "source": [ "## 2 · Adding inertia: integrators and the phase portrait\n", "\n", "Give the free node a mass $m$ and release it from rest at stretch $u_0$. Along the axis, with\n", "$u = l - l_0$, Newton's second law is a harmonic oscillator, $m\\ddot u = -k u$ with\n", "$\\omega = \\sqrt{k/m}$. The exact motion conserves $H = \\tfrac12 k u^2 + \\tfrac12 m v^2$, so in the\n", "displacement–momentum plane $(u,\\,p = mv)$ it traces a **closed ellipse** forever; a good\n", "integrator keeps that loop closed." ] }, { "cell_type": "markdown", "id": "8ab19411", "metadata": {}, "source": [ "`simulate` marches one of simkit's integrators, all fed the same `anchored_spring_system`:\n", "`forward_euler` only reads the force $-\\nabla\\psi$, while `backward_euler` and `bdf2` minimize\n", "$\\psi$ plus an inertia term with Newton (one Newton step is exact here, because $\\psi$ is quadratic\n", "along the axis). Velocities come from the schemes' own difference formulas, and the total energy\n", "$H$ is recorded at every step. The print gives $\\omega$, the period and the number of steps\n", "covering `N_PERIODS` periods." ] }, { "cell_type": "code", "execution_count": 6, "id": "cbd39098", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:34.996652Z", "iopub.status.busy": "2026-09-24T03:44:34.996561Z", "iopub.status.idle": "2026-09-24T03:44:35.035644Z", "shell.execute_reply": "2026-09-24T03:44:35.035238Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "omega = 1.000, period = 6.283, 188 steps of dt = 0.1\n" ] } ], "source": [ "M_osc = MASS * sp.sparse.eye(2).tocsc() # point mass on the free node's two DOFs\n", "omega = np.sqrt(K_SPRING / MASS)\n", "period = 2 * np.pi / omega\n", "n_osc = int(round(N_PERIODS * period / DT_OSC))\n", "\n", "def simulate(scheme):\n", " \"\"\"Release the free mass from rest at stretch U0 and march `scheme`; return u, v and H per step.\"\"\"\n", " x0 = np.array([[SPRING_L0 + U0], [0.0]])\n", " hist = [x0, x0, x0, x0] # position history, newest last: at rest for t <= 0\n", " v = np.zeros((2, 1))\n", " vs = [v]\n", " for _ in range(n_osc):\n", " if scheme == \"Forward Euler\":\n", " x, v = simkit.integrators.forward_euler(hist[-1], v, gradient_func, M_osc, DT_OSC)\n", " elif scheme == \"Backward Euler\":\n", " x = simkit.integrators.backward_euler(hist[-1], hist[-2], energy_func, gradient_func,\n", " hessian_func, M_osc, DT_OSC)\n", " v = simkit.energies.velocity_be(x, hist[-1], DT_OSC)\n", " else:\n", " x = simkit.integrators.bdf2(hist[-1], hist[-2], hist[-3], hist[-4], energy_func, gradient_func,\n", " hessian_func, M_osc, DT_OSC)\n", " v = simkit.energies.velocity_bdf2(x, hist[-1], hist[-2], DT_OSC)\n", " hist.append(x)\n", " vs.append(v)\n", " xs = hist[3:]\n", " u = np.array([x[0, 0] for x in xs]) - SPRING_L0\n", " vel = np.array([v[0, 0] for v in vs])\n", " H_spring = np.array([energy_func(x) for x in xs])\n", " H_kinetic = 0.5 * MASS * vel ** 2\n", " H_total = H_spring + H_kinetic\n", " return {\"u\": u, \"v\": vel, \"H\": H_total}\n", "\n", "traj = {}\n", "for s in SCHEMES:\n", " traj[s] = simulate(s)\n", "print(f\"omega = {omega:.3f}, period = {period:.3f}, {n_osc} steps of dt = {DT_OSC}\")" ] }, { "cell_type": "markdown", "id": "aefe9db5", "metadata": {}, "source": [ "Why they differ: on the state $y = [u, v]$ each scheme is a linear map of $y' = Ay$, with\n", "$A = \\begin{pmatrix}0 & 1\\\\ -k/m & 0\\end{pmatrix}$. The cell builds the maps and prints each one's\n", "per-step amplification (largest eigenvalue magnitude: above 1 grows, below 1 damps). It also\n", "confirms that simkit's trajectories are exactly these maps, to round-off.\n", "\n", "| scheme | one step | phase-space behaviour |\n", "|---|---|---|\n", "| **Forward Euler** | $y_{n+1} = (I + hA)\\,y_n$ | spirals **outward** (gains energy) |\n", "| **Backward Euler** | $(I - hA)\\,y_{n+1} = y_n$ | spirals **inward** (numerical damping) |\n", "| **BDF2** | $(3I - 2hA)\\,y_{n+1} = 4y_n - y_{n-1}$ | **nearly closed** (2nd order) |" ] }, { "cell_type": "code", "execution_count": 7, "id": "250cb79d", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:35.036690Z", "iopub.status.busy": "2026-09-24T03:44:35.036618Z", "iopub.status.idle": "2026-09-24T03:44:35.040274Z", "shell.execute_reply": "2026-09-24T03:44:35.039904Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Forward Euler per-step amplification = 1.00499, max |simkit - map| = 3.3e-16\n", "Backward Euler per-step amplification = 0.99504, max |simkit - map| = 8.5e-15\n", "BDF2 per-step amplification = 0.99998, max |simkit - map| = 5.0e-14\n" ] } ], "source": [ "A = np.array([[0.0, 1.0], [-K_SPRING / MASS, 0.0]])\n", "I2 = np.eye(2)\n", "B = np.linalg.inv(3 * I2 - 2 * DT_OSC * A)\n", "step_maps = {\n", " \"Forward Euler\": I2 + DT_OSC * A,\n", " \"Backward Euler\": np.linalg.inv(I2 - DT_OSC * A),\n", " \"BDF2\": np.block([[4 * B, -B], [I2, np.zeros((2, 2))]]), # acts on [y_n; y_{n-1}]\n", "}\n", "for s, G in step_maps.items():\n", " z = np.tile([U0, 0.0], G.shape[0] // 2) # at rest before release\n", " Y = [z[:2]]\n", " for _ in range(n_osc):\n", " z = G @ z\n", " Y.append(z[:2])\n", " deviation = np.abs(np.array(Y) - np.column_stack([traj[s][\"u\"], traj[s][\"v\"]])).max()\n", " print(f\"{s:15s} per-step amplification = {np.abs(np.linalg.eigvals(G)).max():.5f}, \"\n", " f\"max |simkit - map| = {deviation:.1e}\")" ] }, { "cell_type": "markdown", "id": "1b838b17", "metadata": {}, "source": [ "### The phase portrait\n", "\n", "Displacement against momentum: Forward Euler spirals **out**, Backward Euler spirals **in**, and\n", "BDF2 sits on the exact, energy-conserving ellipse (dashed)." ] }, { "cell_type": "code", "execution_count": 8, "id": "ad578828", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:35.042145Z", "iopub.status.busy": "2026-09-24T03:44:35.041984Z", "iopub.status.idle": "2026-09-24T03:44:35.171990Z", "shell.execute_reply": "2026-09-24T03:44:35.171577Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = utils.phase_plot({s: np.column_stack([traj[s][\"u\"], MASS * traj[s][\"v\"]]) for s in SCHEMES},\n", " xlabel=\"displacement $u = l - l_0$\", ylabel=\"momentum $p = m v$\",\n", " title=f\"Phase portrait of a spring oscillator (dt = {DT_OSC})\",\n", " figsize=(8.4, 6))\n", "theta = np.linspace(0, 2 * np.pi, 200)\n", "ax.plot(U0 * np.cos(theta), MASS * omega * U0 * np.sin(theta), \"k--\", lw=1.2, label=\"exact (conserved)\")\n", "ax.set_aspect(\"equal\")\n", "ax.legend(loc=\"upper left\", bbox_to_anchor=(1.02, 1), fontsize=9) # beside the axes, off the spirals\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"phase_portrait.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"011_phase_portrait.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7bca7daa", "metadata": {}, "source": [ "The same story as a time series of the total energy $H$, which every scheme *should* hold at its\n", "initial value $\\tfrac12 k u_0^2$ (dashed): explicit gains, implicit loses, BDF2 holds." ] }, { "cell_type": "code", "execution_count": 9, "id": "2daa4ecd", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:35.173371Z", "iopub.status.busy": "2026-09-24T03:44:35.173271Z", "iopub.status.idle": "2026-09-24T03:44:35.237900Z", "shell.execute_reply": "2026-09-24T03:44:35.237435Z" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_osc = np.arange(n_osc + 1) * DT_OSC\n", "fig, ax = utils.line_plot(t_osc, {s: traj[s][\"H\"] for s in SCHEMES}, xlabel=\"time (s)\",\n", " ylabel=\"total energy $H$\", colors=utils.INTEGRATOR_COLORS,\n", " title=\"Energy drift: explicit gains, implicit loses, BDF2 holds\")\n", "ax.axhline(0.5 * K_SPRING * U0 ** 2, color=\"0.5\", ls=\"--\", lw=1.2)\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"energy_drift.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"011_energy_drift.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1a40ee59", "metadata": {}, "source": [ "And the three integrators as actual oscillating springs, side by side: the explicit one's swing\n", "grows, the implicit one's shrinks, BDF2's stays steady." ] }, { "cell_type": "code", "execution_count": 10, "id": "6e94bef6", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:35.239423Z", "iopub.status.busy": "2026-09-24T03:44:35.239282Z", "iopub.status.idle": "2026-09-24T03:44:39.688238Z", "shell.execute_reply": "2026-09-24T03:44:39.687623Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stride = max(1, (n_osc + 1) // OSC_FRAMES)\n", "panels = []\n", "for s in SCHEMES:\n", " states = [np.vstack([anchor, [[SPRING_L0 + u, 0.0]]]) for u in traj[s][\"u\"][::stride]]\n", " panels.append({\"states\": states, \"E\": E_spring, \"title\": s})\n", "\n", "fig, anim = utils.animate_springs_grid(\n", " panels, lims=((-0.3, 2.0), (-0.4, 0.4)), fps=FPS, pin_pts=anchor, figsize=(13, 2.6),\n", " suptitle=\"Same spring, same dt: explicit grows, implicit shrinks, BDF2 steady\")\n", "fig.tight_layout()\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"oscillators.mp4\"), fps=FPS,\n", " copy_to=os.path.join(MEDIA_DIR, \"011_oscillators.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "c7b89b9d", "metadata": {}, "source": [ "## 3 · A cable: many springs glued together\n", "\n", "One spring resists only stretch. Chain many end to end and pin both ends, and the assembly\n", "behaves like an elastic **cable**: under gravity the interior masses drop until spring tension\n", "balances weight (an elastic catenary). Springs carry no *bending* stiffness, so this is a cable,\n", "not a beam; bending is the next ingredient. In stacked positions $x$ the cable's potential\n", "$\\Phi$, and the objective of one Backward-Euler step, are\n", "\n", "$$\n", "\\Phi(x) = \\underbrace{\\textstyle\\sum_e \\tfrac12 k\\,(l_e-l_{0,e})^2}_{\\text{springs}}\n", " + \\underbrace{\\tfrac12 x^\\top Q x + b^\\top x}_{\\text{pins}}\n", " - \\underbrace{f_g^\\top x}_{\\text{gravity}},\n", "\\qquad\n", "\\Phi(x) + \\underbrace{\\tfrac{1}{2h^2}\\lVert x - \\tilde x\\rVert_M^2}_{\\text{inertia}},\\quad \\tilde x = 2x_n - x_{n-1}.\n", "$$" ] }, { "cell_type": "markdown", "id": "fb1728fa", "metadata": {}, "source": [ "The cable's constant operators, built once from simkit: the stacked edge-vector operator $J$\n", "($d = Jx$), the rest lengths $l_0$, the lumped mass matrix $M$, the gravity force $f_g$ and the\n", "soft-pin penalty $(Q, b)$ from `dirichlet_penalty`. The print checks that the lumped masses add\n", "up to $\\rho L$ and the weights to $\\rho L g$." ] }, { "cell_type": "code", "execution_count": 11, "id": "15eb15c5", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:39.690070Z", "iopub.status.busy": "2026-09-24T03:44:39.689919Z", "iopub.status.idle": "2026-09-24T03:44:39.694521Z", "shell.execute_reply": "2026-09-24T03:44:39.694207Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "J: (40, 42), total mass = 4.000 (rho L = 4.000), total weight = -39.200 (rho L g = -39.200)\n" ] } ], "source": [ "J = sp.sparse.kron(simkit.edge_displacement_jacobian(X, E), sp.sparse.eye(dim)).tocsc() # d = J x\n", "l0 = simkit.edge_lengths(X, E).reshape(-1, 1) # rest length of every spring\n", "vol = np.ones((len(E), 1)) # unit weight per spring\n", "M_nodes = simkit.massmatrix(X, E, rho=RHO) # lumped mass of every node\n", "M = sp.sparse.kron(M_nodes, sp.sparse.eye(dim)).tocsc() # the same mass on every DOF\n", "f_g = simkit.gravity_force(X, E, a=GRAVITY, rho=RHO).reshape(-1, 1) # weight of every node\n", "Q_pin, b_pin = simkit.dirichlet_penalty(pin_idx, X[pin_idx], n, K_PIN) # soft pins at both ends\n", "print(f\"J: {J.shape}, total mass = {M_nodes.sum():.3f} (rho L = {RHO * CABLE_LENGTH:.3f}), \"\n", " f\"total weight = {f_g.sum():.3f} (rho L g = {RHO * CABLE_LENGTH * GRAVITY:.3f})\")" ] }, { "cell_type": "markdown", "id": "c369959d", "metadata": {}, "source": [ "`cable_system` closes over those operators and builds every term from simkit, one per line: the\n", "springs with `mass_springs_*_z` on $d = Jx$, the pins as a quadratic, and gravity as a linear\n", "term. Called without a previous state it is the quasi-static potential $\\Phi$; given\n", "$(x_n, x_{n-1})$ it adds the Backward-Euler inertia term (`kinetic_*_be`), so one function drives\n", "both runs." ] }, { "cell_type": "code", "execution_count": 12, "id": "049034e2", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:39.695974Z", "iopub.status.busy": "2026-09-24T03:44:39.695893Z", "iopub.status.idle": "2026-09-24T03:44:39.698746Z", "shell.execute_reply": "2026-09-24T03:44:39.698362Z" } }, "outputs": [], "source": [ "def cable_system(k, x_curr=None, x_prev=None, h=DT):\n", " \"\"\"Cable potential (springs + pins + gravity) with spring stiffness k, in stacked positions x.\n", "\n", " Closes over the constant operators J, l0, vol, M, f_g, Q_pin, b_pin built above.\n", " Pass x_curr, x_prev to add the Backward-Euler inertia term.\"\"\"\n", " ym = np.full((len(E), 1), k)\n", " dynamic = x_curr is not None\n", "\n", " def energy_func(x):\n", " E_spring = simkit.energies.mass_springs_energy_z(x, J, ym, vol, l0)\n", " E_pin = simkit.energies.quadratic_energy(x, Q_pin, b_pin)\n", " E_gravity = -(f_g.T @ x).item()\n", " E_inertia = simkit.energies.kinetic_energy_be(x, x_curr, x_prev, M, h) if dynamic else 0.0\n", " E_total = E_spring + E_pin + E_gravity + E_inertia\n", " return E_total\n", "\n", " def gradient_func(x):\n", " g_spring = simkit.energies.mass_springs_gradient_z(x, J, ym, vol, l0)\n", " g_pin = simkit.energies.quadratic_gradient(x, Q_pin, b_pin)\n", " g_gravity = -f_g\n", " g_inertia = simkit.energies.kinetic_gradient_be(x, x_curr, x_prev, M, h) if dynamic else 0.0\n", " g_total = g_spring + g_pin + g_gravity + g_inertia\n", " return g_total\n", "\n", " def hessian_func(x):\n", " H_spring = simkit.energies.mass_springs_hessian_z(x, J, ym, vol, l0, psd=True)\n", " H_pin = simkit.energies.quadratic_hessian(Q_pin)\n", " H_inertia = simkit.energies.kinetic_hessian_be(M, h) if dynamic else 0.0 * M\n", " H_total = H_spring + H_pin + H_inertia # gravity is linear: no Hessian term\n", " return H_total\n", "\n", " return energy_func, gradient_func, hessian_func" ] }, { "cell_type": "markdown", "id": "8d8e722e", "metadata": {}, "source": [ "Before trusting Newton with it, check the gradient of the full dynamic system (all four terms)\n", "against central differences of its energy (`simkit.gradient_cfd`) at a random stretched state.\n", "The relative error should be tiny." ] }, { "cell_type": "code", "execution_count": 13, "id": "9b615cd3", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:39.699757Z", "iopub.status.busy": "2026-09-24T03:44:39.699676Z", "iopub.status.idle": "2026-09-24T03:44:39.705491Z", "shell.execute_reply": "2026-09-24T03:44:39.705152Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "relative gradient error vs central differences: 6.7e-08\n" ] } ], "source": [ "x_rest = X.reshape(-1, 1).copy()\n", "rng = np.random.default_rng(SEED)\n", "noise = FD_NOISE * rng.standard_normal((n, dim))\n", "noise[pin_idx] = 0.0 # keep the pins on target\n", "x_test = (X + noise).reshape(-1, 1)\n", "\n", "step_energy, step_gradient, _ = cable_system(K_CABLE, x_curr=x_rest, x_prev=x_rest)\n", "g_fd = simkit.gradient_cfd(lambda y: np.array(step_energy(y.reshape(-1, 1))), x_test.ravel(), FD_STEP)\n", "g = step_gradient(x_test)\n", "print(f\"relative gradient error vs central differences: {np.linalg.norm(g - g_fd.reshape(-1, 1)) / np.linalg.norm(g):.1e}\")" ] }, { "cell_type": "markdown", "id": "0e676d61", "metadata": {}, "source": [ "### Without inertia: static equilibrium via Newton\n", "\n", "No time, no velocity: minimize $\\Phi$ from the flat chain, one Newton step at a time, recording\n", "every iterate until the step is below `NEWTON_TOL`. The chain drops into its sag within a few\n", "iterations while the energy gap $\\Phi_k - \\Phi^\\star$ collapses to zero." ] }, { "cell_type": "code", "execution_count": 14, "id": "6eeac958", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:39.706435Z", "iopub.status.busy": "2026-09-24T03:44:39.706375Z", "iopub.status.idle": "2026-09-24T03:44:39.944407Z", "shell.execute_reply": "2026-09-24T03:44:39.944030Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "static: 7 Newton iterations, |grad| = 4.5e-11, max sag = 1.258\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "phi_energy, phi_gradient, phi_hessian = cable_system(K_CABLE)\n", "\n", "x = x_rest.copy()\n", "static_states, phi_hist, grad_hist = [X.copy()], [phi_energy(x)], [np.linalg.norm(phi_gradient(x))]\n", "for _ in range(NEWTON_MAX_ITERS):\n", " x_next = newton_solver(x, phi_energy, phi_gradient, phi_hessian, max_iter=1)\n", " step = np.linalg.norm(x_next - x)\n", " x = x_next\n", " static_states.append(x.reshape(n, dim).copy())\n", " phi_hist.append(phi_energy(x))\n", " grad_hist.append(np.linalg.norm(phi_gradient(x)))\n", " if step < NEWTON_TOL:\n", " break\n", "x_static = x.copy()\n", "phi_star = phi_hist[-1]\n", "energy_gap = np.array(phi_hist) - phi_star\n", "print(f\"static: {len(static_states) - 1} Newton iterations, |grad| = {grad_hist[-1]:.1e}, \"\n", " f\"max sag = {-x_static.reshape(n, dim)[:, 1].min():.3f}\")\n", "\n", "fig, anim = utils.animate_springs_energy(\n", " static_states, E, np.arange(len(static_states)), {\"potential\": energy_gap}, rest=X, lims=CABLE_LIMS,\n", " xlabel=\"Newton iteration\", ylabel=r\"energy gap $\\Phi_k - \\Phi^\\star$\", scene_title=\"static sag (gray = rest)\",\n", " title=\"energy minimized\", colors={\"potential\": utils.ENERGY_COLORS[\"potential\"]}, pin_pts=X[pin_idx])\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"cable_static.mp4\"), fps=NEWTON_FPS,\n", " copy_to=os.path.join(MEDIA_DIR, \"011_cable_static.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "88500b0d", "metadata": {}, "source": [ "The same solve on a log scale. The first step overshoots the sag (the line search only asks for\n", "lower energy), so the gradient norm briefly rises; after that both curves fall ever faster, the\n", "last steps quadratically, down to round-off." ] }, { "cell_type": "code", "execution_count": 15, "id": "0d994d32", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:39.945667Z", "iopub.status.busy": "2026-09-24T03:44:39.945570Z", "iopub.status.idle": "2026-09-24T03:44:40.098011Z", "shell.execute_reply": "2026-09-24T03:44:40.097682Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax_g, ax_e) = plt.subplots(1, 2, figsize=(11, 4))\n", "utils.residual_plot({\"Newton\": grad_hist}, ax=ax_g, markers=True, xlabel=\"Newton iteration\",\n", " ylabel=r\"$\\|\\nabla\\Phi(x_k)\\|$\", title=\"gradient norm\")\n", "utils.residual_plot({\"Newton\": energy_gap}, ax=ax_e, markers=True, xlabel=\"Newton iteration\",\n", " ylabel=r\"$\\Phi_k - \\Phi^\\star$\", title=\"energy gap\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"newton_convergence.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"011_newton_convergence.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "955c7053", "metadata": {}, "source": [ "Two scalar fields of the cable: the lumped mass of each node (the two end nodes own half a spring\n", "each, so they get half the mass), and the tension $k\\,(l_e - l_{0,e})$ of each spring at the\n", "static equilibrium. The tension is largest next to the pins, which carry the whole weight, and\n", "smallest at the bottom." ] }, { "cell_type": "code", "execution_count": 16, "id": "0fd03620", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:40.099055Z", "iopub.status.busy": "2026-09-24T03:44:40.098984Z", "iopub.status.idle": "2026-09-24T03:44:40.238650Z", "shell.execute_reply": "2026-09-24T03:44:40.238226Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "tension: 14.4 at the bottom -> 23.5 next to the pins\n" ] } ], "source": [ "m_nodes = M_nodes.diagonal()\n", "X_static = x_static.reshape(n, dim)\n", "tension = K_CABLE * (simkit.edge_lengths(X_static, E) - l0.ravel())\n", "\n", "fig, (ax_m, ax_t) = plt.subplots(2, 1, figsize=(8, 6.6), gridspec_kw={\"height_ratios\": [1, 2.6]})\n", "utils.plot_spring_network(ax_m, X, E, node_values=m_nodes, node_size=70, cmap=\"viridis\",\n", " title=\"lumped node mass (at rest)\", label=\"mass\", vmin=0.0,\n", " lims=(CABLE_LIMS[0], (-0.5, 0.5)))\n", "utils.plot_spring_network(ax_t, X_static, E, edge_values=tension, pins=pin_idx, node_size=20, lw=3,\n", " cmap=\"plasma\", title=\"spring tension at equilibrium\", label=r\"$k(l-l_0)$\",\n", " lims=CABLE_LIMS)\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"cable_fields.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"011_cable_fields.png\"))\n", "plt.show()\n", "print(f\"tension: {tension.min():.1f} at the bottom -> {tension.max():.1f} next to the pins\")" ] }, { "cell_type": "markdown", "id": "74a35a09", "metadata": {}, "source": [ "### With inertia: Backward-Euler dynamics from rest\n", "\n", "Release the flat chain and march it `N_STEPS` steps: each step rebuilds `cable_system` with the\n", "last two states and minimizes it with Newton, starting from the inertial guess $\\tilde x$. The chain\n", "falls, overshoots and oscillates, and Backward Euler's numerical damping rings the kinetic energy\n", "down." ] }, { "cell_type": "code", "execution_count": 17, "id": "0dbde0f1", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:40.239807Z", "iopub.status.busy": "2026-09-24T03:44:40.239682Z", "iopub.status.idle": "2026-09-24T03:44:47.324184Z", "shell.execute_reply": "2026-09-24T03:44:47.323802Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "dynamic: max sag during the run = 1.981, final max sag = 1.268 (static 1.258), final KE = 1.7e-04\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x_curr, x_prev = x_rest.copy(), x_rest.copy() # released from rest\n", "dyn_states = [X.copy()]\n", "ke_hist = [0.0] # kinetic energy\n", "dist_hist = [np.linalg.norm((x_rest - x_static).reshape(n, dim), axis=1).max()] # largest node distance to x*\n", "total_hist = [phi_hist[0] - phi_star] # kinetic + potential above the minimum\n", "for _ in range(N_STEPS):\n", " step_energy, step_gradient, step_hessian = cable_system(K_CABLE, x_curr=x_curr, x_prev=x_prev)\n", " x_tilde = simkit.energies.be_target(x_curr, x_prev, DT)\n", " x_next = newton_solver(x_tilde, step_energy, step_gradient, step_hessian, max_iter=STEP_ITERS,\n", " tolerance=STEP_TOL)\n", " x_prev, x_curr = x_curr, x_next\n", " v = simkit.energies.velocity_be(x_curr, x_prev, DT)\n", " ke = 0.5 * (v.T @ M @ v).item() # kinetic energy\n", " pe = phi_energy(x_curr) - phi_star # potential above the minimum\n", " total = ke + pe\n", " dyn_states.append(x_curr.reshape(n, dim).copy())\n", " ke_hist.append(ke)\n", " dist_hist.append(np.linalg.norm((x_curr - x_static).reshape(n, dim), axis=1).max())\n", " total_hist.append(total)\n", "t_hist = np.arange(N_STEPS + 1) * DT\n", "print(f\"dynamic: max sag during the run = {max(-s[:, 1].min() for s in dyn_states):.3f}, \"\n", " f\"final max sag = {-x_curr.reshape(n, dim)[:, 1].min():.3f} (static {-X_static[:, 1].min():.3f}), \"\n", " f\"final KE = {ke_hist[-1]:.1e}\")\n", "\n", "fig, anim = utils.animate_springs_energy(\n", " dyn_states, E, t_hist, {\"kinetic\": ke_hist}, rest=X,\n", " lims=CABLE_LIMS, xlabel=\"time (s)\", ylabel=\"kinetic energy\", scene_title=\"dynamic sag (Backward Euler)\",\n", " title=\"kinetic energy rings down\", colors={\"kinetic\": utils.ENERGY_COLORS[\"kinetic\"]}, pin_pts=X[pin_idx])\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"cable_dynamic.mp4\"), fps=CABLE_FPS,\n", " copy_to=os.path.join(MEDIA_DIR, \"011_cable_dynamic.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "9796e9b2", "metadata": {}, "source": [ "### Same equilibrium, two roads\n", "\n", "Quasi-static minimization (each Newton iterate held for a few frames) and full dynamics, side by\n", "side: both settle to the **same** sagged shape." ] }, { "cell_type": "code", "execution_count": 18, "id": "a780b58d", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:47.325846Z", "iopub.status.busy": "2026-09-24T03:44:47.325776Z", "iopub.status.idle": "2026-09-24T03:44:49.473813Z", "shell.execute_reply": "2026-09-24T03:44:49.473392Z" } }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "static_frames = [static_states[min(i * len(static_states) // COMPARE_FRAMES, len(static_states) - 1)]\n", " for i in range(COMPARE_FRAMES)]\n", "dynamic_frames = [dyn_states[i] for i in np.linspace(0, N_STEPS, COMPARE_FRAMES).astype(int)]\n", "\n", "fig, anim = utils.animate_springs_grid(\n", " [{\"states\": static_frames, \"E\": E, \"title\": \"without inertia (Newton iterates)\"},\n", " {\"states\": dynamic_frames, \"E\": E, \"title\": \"with inertia (Backward Euler)\"}],\n", " lims=CABLE_LIMS, fps=FPS, pin_pts=X[pin_idx], figsize=(11, 3.8),\n", " suptitle=\"Cable sag: minimization vs dynamics settle to the same shape\")\n", "video = simkit.filesystem.save_animation(anim, os.path.join(RESULTS_DIR, \"cable_compare.mp4\"), fps=FPS,\n", " copy_to=os.path.join(MEDIA_DIR, \"011_cable_compare.mp4\"))\n", "plt.close(fig)\n", "utils.embed_video(video)" ] }, { "cell_type": "markdown", "id": "ddd77cc2", "metadata": {}, "source": [ "Quantitatively: the largest vertex distance between the dynamic cable and the static equilibrium,\n", "and the total energy above the static minimum, $\\tfrac12 v^\\top M v + \\Phi(x) - \\Phi^\\star$. Both\n", "decay toward zero, and the total energy never increases: Backward Euler only removes energy." ] }, { "cell_type": "code", "execution_count": 19, "id": "94cef030", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:49.475048Z", "iopub.status.busy": "2026-09-24T03:44:49.474956Z", "iopub.status.idle": "2026-09-24T03:44:49.753346Z", "shell.execute_reply": "2026-09-24T03:44:49.752870Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "total energy monotone (up to round-off): True, final distance = 1.0e-02\n" ] } ], "source": [ "fig, (ax_d, ax_h) = plt.subplots(1, 2, figsize=(11, 4))\n", "utils.residual_plot({\"dynamic\": dist_hist}, t_hist, ax=ax_d, xlabel=\"time (s)\",\n", " ylabel=r\"$\\max_i \\|x_i(t) - x_i^\\star\\|$\", title=\"distance to the static shape\")\n", "utils.residual_plot({\"dynamic\": total_hist}, t_hist, ax=ax_h, xlabel=\"time (s)\",\n", " ylabel=r\"$\\frac{1}{2}v^\\top M v + \\Phi - \\Phi^\\star$\", title=\"total energy above the minimum\")\n", "fig.tight_layout()\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"cable_settling.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"011_cable_settling.png\"))\n", "plt.show()\n", "print(f\"total energy monotone (up to round-off): {bool(np.all(np.diff(total_hist) <= MONOTONE_TOL))}, \"\n", " f\"final distance = {dist_hist[-1]:.1e}\")" ] }, { "cell_type": "markdown", "id": "5322e7f6", "metadata": {}, "source": [ "Finally, a quick parameter study: re-solve the static sag for each stiffness in `K_SWEEP`. Softer\n", "springs stretch more and sag deeper." ] }, { "cell_type": "code", "execution_count": 20, "id": "33fc5917", "metadata": { "execution": { "iopub.execute_input": "2026-09-24T03:44:49.754934Z", "iopub.status.busy": "2026-09-24T03:44:49.754766Z", "iopub.status.idle": "2026-09-24T03:44:49.830533Z", "shell.execute_reply": "2026-09-24T03:44:49.830214Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k = 100: max sag = 2.374\n", "k = 400: max sag = 1.258\n", "k = 1600: max sag = 0.744\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sags = {}\n", "for k in K_SWEEP:\n", " energy_k, gradient_k, hessian_k = cable_system(k)\n", " x_k = newton_solver(x_rest.copy(), energy_k, gradient_k, hessian_k, max_iter=NEWTON_MAX_ITERS, tolerance=NEWTON_TOL)\n", " sags[k] = x_k.reshape(n, dim)\n", " print(f\"k = {k:6g}: max sag = {-sags[k][:, 1].min():.3f}\")\n", "\n", "fig, ax = plt.subplots(figsize=(7, 4.5))\n", "utils.setup_axes(ax, *CABLE_LIMS, title=\"Softer springs sag more\")\n", "cmap = plt.get_cmap(\"viridis\")\n", "for j, (k, X_k) in enumerate(sags.items()):\n", " ax.plot(X_k[:, 0], X_k[:, 1], \"-o\", ms=4, lw=2, color=cmap(j / max(1, len(sags) - 1)), label=f\"k = {k:g}\")\n", "ax.scatter(X[pin_idx, 0], X[pin_idx, 1], s=70, marker=\"s\", color=utils.PIN_C, zorder=5, label=\"pinned\")\n", "ax.legend(fontsize=9, loc=\"lower right\")\n", "simkit.filesystem.save_figure(fig, os.path.join(RESULTS_DIR, \"cable_stiffness.png\"),\n", " copy_to=os.path.join(MEDIA_DIR, \"011_cable_stiffness.png\"))\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "87161acf", "metadata": {}, "source": [ "### Takeaways\n", "* A spring stores $\\tfrac12 k (l-l_0)^2$; differentiating gives the linear **Hooke force**\n", " $-k(l-l_0)$.\n", "* With inertia the integrator decides the energy behaviour: **Forward Euler** gains it (unstable),\n", " **Backward Euler** bleeds it (damped), **BDF2** nearly conserves it, vivid in the phase portrait.\n", "* Many springs make an elastic **cable**; gravity sags it into an elastic catenary, and the\n", " quasi-static minimization and the dynamic Backward-Euler run settle to the **same** equilibrium." ] } ], "metadata": { "kernelspec": { "display_name": "simkit", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }