{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lagrangian mechanics\n", "\n", "> Marcos Duarte \n", "> [Laboratory of Biomechanics and Motor Control](http://pesquisa.ufabc.edu.br/bmclab) \n", "> Federal University of ABC, Brazil" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"The theoretical development of the laws of motion of bodies is a problem of such interest and importance, that it has engaged the attention of all the most eminent mathematicians, since the invention of dynamics as a mathematical science by Galileo, and especially since the wonderful extension which was given to that science by Newton. Among the successors of those illustrious men, Lagrange has perhaps done more than any other analyst, to give extent and harmony to such deductive researches, by showing that the most varied consequences respecting the motions of systems of bodies may be derived from one radical formula; the beauty of the method so suiting the dignity of the results, as to make of his great work a kind of scientific poem.\"   Hamilton (1834)\n", "
" ] }, { "cell_type": "markdown", "metadata": { "toc": 1 }, "source": [ "

# Contents

\n", "
" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2020-06-14T19:57:05.634688Z", "start_time": "2020-06-14T19:57:03.823843Z" } }, "outputs": [], "source": [ "# import necessary libraries and configure environment\n", "import numpy as np\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "sns.set_context('notebook', font_scale=1.2, rc={\"lines.linewidth\": 2})\n", "# import Sympy functions\n", "import sympy as sym\n", "from sympy import Symbol, symbols, cos, sin, Matrix, simplify, Eq, latex, expand\n", "from sympy.solvers.solveset import nonlinsolve\n", "from sympy.physics.mechanics import dynamicsymbols, mlatex, init_vprinting\n", "init_vprinting()\n", "from IPython.display import display, Math" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "We know that some problems in dynamics can be solved using the principle of conservation of mechanical energy, that the total mechanical energy in a system (the sum of potential and kinetic energies) is constant when only conservative forces are present in the system. Such approach is one kind of energy methods, see for example, pages 495-512 in Ruina and Pratap (2019). \n", "\n", "Lagrangian mechanics (after [Joseph-Louis Lagrange](https://en.wikipedia.org/wiki/Joseph-Louis_Lagrange)) can be seen as another kind of energy methods, but much more general, to the extent is an alternative to Newtonian mechanics. \n", "\n", "The Lagrangian mechanics is a formulation of classical mechanics where the equations of motion are obtained from the kinetic and potential energy of the system (scalar quantities) represented in generalized coordinates instead of using Newton's laws of motion to deduce the equations of motion from the forces on the system (vector quantities) represented in Cartesian coordinates. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generalized coordinates\n", "\n", "The direct application of Newton's laws to mechanical systems results in a set of equations of motion in terms of Cartesian coordinates of each of the particles that make up the system. In many cases, this is not the most convenient coordinate system to solve the problem or describe the movement of the system. For example, for a serial chain of rigid links, such as a member of the human body or from a robot manipulator, it may be simpler to describe the positions of each link by the angles between links. \n", "\n", "Coordinate systems such as angles of a chain of links are referred as [generalized coordinates](https://en.wikipedia.org/wiki/Generalized_coordinates). Generalized coordinates uniquely specify the positions of the particles in a system. Although there may be several generalized coordinates to describe a system, usually a judicious choice of generalized coordinates provides the minimum number of independent coordinates that define the configuration of a system (which is the number of degrees of freedom of the system), turning the problem simpler to solve. In this case, when the number of generalized coordinates equals the number of degrees of freedom, the system is referred as a holonomic system. In a non-holonomic system, the number of generalized coordinates necessary do describe the system depends on the path taken by the system. \n", "\n", "Being a little more technical, according to [Wikipedia](https://en.wikipedia.org/wiki/Configuration_space_(physics)): \n", "\"In classical mechanics, the parameters that define the configuration of a system are called generalized coordinates, and the vector space defined by these coordinates is called the configuration space of the physical system. It is often the case that these parameters satisfy mathematical constraints, such that the set of actual configurations of the system is a manifold in the space of generalized coordinates. This manifold is called the configuration manifold of the system.\"\n", "\n", "In problems where it is desired to use generalized coordinates, one can write Newton's equations of motion in terms of Cartesian coordinates and then transform them into generalized coordinates. However, it would be desirable and convenient to have a general method that would directly establish the equations of motion in terms of a set of convenient generalized coordinates. In addition, general methods for writing, and perhaps solving, the equations of motion in terms of any coordinate system would also be desirable. The [Lagrangian mechanics](https://en.wikipedia.org/wiki/Lagrangian_mechanics) is such a method." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Euler–Lagrange equations\n", "\n", "\n", "See [this notebook](http://nbviewer.jupyter.org/github/BMClab/bmc/blob/master/notebooks/lagrangian_mechanics_generalized.ipynb) for a deduction of the Lagrange's equation in generalized coordinates.\n", "\n", "Consider a system whose configuration (positions) can be described by a set of $N$ generalized coordinates $q_i\\,(i=1,\\dotsc,N)$.\n", "\n", "Let's define the Lagrange or Lagrangian function $\\mathcal{L}$ as the difference between the total kinetic energy $T$ and the total potential energy $V$ of the system in terms of the generalized coordinates as:\n", "

\n", "\n", "\$$\n", "\\mathcal{L}(t,q,\\dot{q}) = T(\\dot{q}_1(t),\\dotsc,\\dot{q}_N(t)) - V(q_1(t),\\dotsc,q_N(t))\n", "\\label{}\n", "\$$\n", "\n", " \n", "where the total potential energy is only due to conservative forces, that is, forces in which the total work done to move the system between two points is independent of the path taken.\n", " \n", "The Euler–Lagrange equations (or Lagrange's equations of the second kind) of the system are (omitting the functions' dependencies for sake of clarity):\n", "

\n", "\n", "\$$\n", "\\frac{\\mathrm d }{\\mathrm d t}\\left( {\\frac{\\partial \\mathcal{L}}{\\partial \\dot{q}_i }} \n", "\\right)-\\frac{\\partial \\mathcal{L}}{\\partial q_i } = Q_{NCi} \\quad i=1,\\dotsc,N\n", "\\label{}\n", "\$$\n", " \n", " \n", "where $Q_{NCi}$ are the generalized forces due to non-conservative forces acting on the system, any forces that can't be expressed in terms of a potential. \n", "\n", "Once all derivatives of the Lagrangian function are calculated and substitute them in the equations above, the result is the equation of motion (EOM) for each generalized coordinate. There will be $N$ equations for a system with $N$ generalized coordinates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Steps to deduce the Euler-Lagrange equations\n", "\n", "1. Model the problem. Define the number of degrees of freedom. Carefully select the corresponding generalized coordinates to describe the system;\n", "2. Calculate the total kinetic and total potential energies of the system. Calculate the Lagrangian;\n", "3. Calculate the generalized forces for each generalized coordinate;\n", "4. For each generalized coordinate, calculate the three derivatives present on the left side of the Euler-Lagrange equation;\n", "5. For each generalized coordinate, substitute the result of these three derivatives in the left side and the corresponding generalized forces in the right side of the Euler-Lagrange equation.\n", "\n", "The EOM's, one for each generalized coordinate, are the result of the last step." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Particle moving under the influence of a conservative force\n", "\n", "Let's deduce the EOM of a particle with mass $m$ moving in the three-dimensional space under the influence of a [conservative force](https://en.wikipedia.org/wiki/Conservative_force). \n", "\n", "The model is the particle moving in 3D space and there is no generalized force (non-conservative force); the particle has three degrees of freedom and we need three generalized coordinates, which can be $(x, y, z)$, where $y$ is vertical, in a Cartesian frame of reference. \n", "The Lagrangian $(\\mathcal{L} = T - V)$ of the particle is:\n", "

\n", "\n", "\$$\n", "\\mathcal{L} = \\frac{1}{2}m(\\dot x^2(t) + \\dot y^2(t) + \\dot z^2(t)) - V(x(t),y(t),z(t)) \n", "\\label{}\n", "\$$\n", "\n", "\n", "The equations of motion for the particle are found by applying the Euler–Lagrange equation for each coordinate. \n", "For the $x$ coordinate:\n", "

\n", "\n", "\$$\n", "\\frac{\\mathrm d }{\\mathrm d t}\\left( {\\frac{\\partial \\mathcal{L}}{\\partial \\dot{x}}} \n", "\\right) - \\frac{\\partial \\mathcal{L}}{\\partial x } = 0\n", "\\label{}\n", "\$$\n", "\n", "\n", "And the derivatives are:\n", "

\n", "\n", "\$$\\begin{array}{rcl}\n", "&\\dfrac{\\partial \\mathcal{L}}{\\partial x} &=& -\\dfrac{\\partial V}{\\partial x} \\\\\n", "&\\dfrac{\\partial \\mathcal{L}}{\\partial \\dot{x}} &=& m\\dot{x} \\\\\n", "&\\dfrac{\\mathrm d }{\\mathrm d t}\\left( {\\dfrac{\\partial \\mathcal{L}}{\\partial \\dot{x}}} \\right) &=& m\\ddot{x} \n", "\\end{array}\n", "\\label{}\n", "\$$\n", "\n", "\n", "Finally, the EOM is:\n", "

\n", "\n", "\$$\\begin{array}{l}\n", "m\\ddot{x} + \\dfrac{\\partial V}{\\partial x} = 0 \\quad \\rightarrow \\\\\n", "m\\ddot{x} = -\\dfrac{\\partial V}{\\partial x} \n", "\\end{array}\n", "\\label{}\n", "\$$\n", "\n", "\n", "and same procedure for the $y$ and $z$ coordinates. \n", "\n", "The equation above is the Newton's second law of motion.\n", "\n", "For instance, if the conservative force is due to the gravitational field near Earth's surface $(V=[0, mgy, 0])$, the Euler–Lagrange equations (the EOM's) are:\n", "

\n", "\n", "\$$\\begin{array}{rcl}\n", "m\\ddot{x} &=& -\\dfrac{\\partial (0)}{\\partial x} &=& 0 \\\\\n", "m\\ddot{y} &=& -\\dfrac{\\partial (mgy)}{\\partial y} &=& -mg \\\\\n", "m\\ddot{z} &=& -\\dfrac{\\partial (0)}{\\partial z} &=& 0 \n", "\\end{array}\n", "\\label{}\n", "\$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Ideal mass-spring system\n", "\n", "

\n", "\n", "Consider a system with a mass $m$ attached to an ideal spring (massless, length $\\ell_0$, and spring constant $k$) at the horizontal direction $x$. A force is momentarily applied to the mass and then the system is left unperturbed. \n", "Let's deduce the EOM of this system. \n", "\n", "The system can be modeled as a particle attached to a spring moving at the direction $x$, the only generalized coordinate needed (with origin of the Cartesian reference frame at the wall where the spring is attached), and there is no generalized force. \n", "The Lagrangian $(\\mathcal{L} = T - V)$ of the system is: \n", "

\n", "\n", "\$$\n", "\\mathcal{L} = \\frac{1}{2}m\\dot x^2 - \\frac{1}{2}k(x-\\ell_0)^2\n", "\\label{}\n", "\$$\n", "\n", "\n", "And the derivatives are:\n", "

\n", "\n", "\$$\\begin{array}{rcl}\n", "&\\dfrac{\\partial \\mathcal{L}}{\\partial x} &=& -k(x-\\ell_0) \\\\\n", "&\\dfrac{\\partial \\mathcal{L}}{\\partial \\dot{x}} &=& m\\dot{x} \\\\\n", "&\\dfrac{\\mathrm d }{\\mathrm d t}\\left( {\\dfrac{\\partial \\mathcal{L}}{\\partial \\dot{x}}} \\right) &=& m\\ddot{x} \n", "\\end{array} \n", "\$$\n", "\n", "\n", "Finally, the Euler–Lagrange equation (the EOM) is:\n", "

\n", "\n", "\$$\n", "m\\ddot{x} + k(x-\\ell_0) = 0\n", "\\label{}\n", "\$$\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Simple pendulum under the influence of gravity\n", "\n", "

\n", "\n", "Consider a pendulum with a massless rod of length $d$ and a mass $m$ at the extremity swinging in a plane forming the angle $\\theta$ with the vertical. \n", "Let's deduce the EOM of this system.\n", "\n", "The model is a particle oscillating as a pendulum under a constant gravitational force $-mg$. \n", "Although the pendulum moves at the plane, it only has one degree of freedom, which can be described by the angle $\\theta$, the generalized coordinate. Let's adopt the origin of the reference frame at the point of the pendulum suspension. \n", "\n", "The kinetic energy of the system is:\n", "

\n", "\n", "\$$\n", "T = \\frac{1}{2}mv^2 = \\frac{1}{2}m(\\dot{x}^2+\\dot{y}^2)\n", "\$$\n", "\n", "\n", "where $\\dot{x}$ and $\\dot{y}$ are:\n", "

\n", "\n", "\$$\\begin{array}{l}\n", "x = d\\sin(\\theta) \\\\\n", "y = -d\\cos(\\theta) \\\\ \n", "\\dot{x} = d\\cos(\\theta)\\dot{\\theta} \\\\\n", "\\dot{y} = d\\sin(\\theta)\\dot{\\theta}\n", "\\end{array} \$$\n", "\n", "\n", "Consequently, the kinetic energy is:\n", "

\n", "\n", "\$$\n", "T = \\frac{1}{2}m\\left((d\\cos(\\theta)\\dot{\\theta})^2 + (d\\sin(\\theta)\\dot{\\theta})^2\\right) = \\frac{1}{2}md^2\\dot{\\theta}^2\n", "\$$\n", " \n", "\n", "And the potential energy of the system is:\n", "

\n", "\n", "\$$\n", "V = -mgy = -mgd\\cos\\theta\n", "\$$\n", "\n", " \n", "The Lagrangian function is:\n", "

\n", "\n", "\$$\n", "\\mathcal{L} = \\frac{1}{2}md^2\\dot\\theta^2 + mgd\\cos\\theta\n", "\$$\n", "\n", " \n", "And the derivatives are:\n", "

\n", "\n", "\$$\\begin{array}{rcl}\n", "&\\dfrac{\\partial \\mathcal{L}}{\\partial \\theta} &=& -mgd\\sin\\theta \\\\\n", "&\\dfrac{\\partial \\mathcal{L}}{\\partial \\dot{\\theta}} &=& md^2\\dot{\\theta} \\\\\n", "&\\dfrac{\\mathrm d }{\\mathrm d t}\\left( {\\dfrac{\\partial \\mathcal{L}}{\\partial \\dot{\\theta}}} \\right) &=& md^2\\ddot{\\theta}\n", "\\end{array} \$$\n", "\n", " \n", "Finally, the Euler–Lagrange equation (the EOM) is:\n", "

\n", "\n", "\$$\n", "md^2\\ddot\\theta + mgd\\sin\\theta = 0\n", "\$$\n", "\n", " \n", "Note that although the generalized coordinate of the system is $\\theta$, we had to employ Cartesian coordinates at the beginning to derive expressions for the kinetic and potential energies. For kinetic energy, we could have used its equivalent definition for circular motion $(T=I\\dot{\\theta}^2/2=md^2\\dot{\\theta}^2/2)$, but for the potential energy there is no other way since the gravitational force acts in the vertical direction.\n", "In cases like this, a fundamental aspect is to express the Cartesian coordinates in terms of the generalized coordinates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Numerical solution of the equation of motion for the simple pendulum\n", "\n", "A classical approach to solve analytically the EOM for the simple pendulum is to consider the motion for small angles where $\\sin\\theta \\approx \\theta$ and the differential equation is linearized to $d\\ddot\\theta + g\\theta = 0$. This equation has an analytical solution of the type $\\theta(t) = A \\sin(\\omega t + \\phi)$, where $\\omega = \\sqrt{g/d}$ and $A$ and $\\phi$ are constants related to the initial position and velocity. \n", "For didactic purposes, let's solve numerically the differential equation for the pendulum using [Euler’s method](https://nbviewer.jupyter.org/github/demotu/BMC/blob/master/notebooks/OrdinaryDifferentialEquation.ipynb#Euler-method). \n", "\n", "Remember that we have to: \n", "1. Transform the second-order ODE into two coupled first-order ODEs, \n", "2. Approximate the derivative of each variable by its discrete first order difference \n", "3. Write an equation to calculate the variable in a recursive way, updating its value with an equation based on the first order difference. \n", "\n", "We will also implement different variations of the Euler method: Forward (standard), Semi-implicit, and Semi-implicit variation (same results as Semi-implicit). \n", "\n", "Implementing these steps in Python: " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2020-06-14T19:57:53.324379Z", "start_time": "2020-06-14T19:57:53.298346Z" } }, "outputs": [], "source": [ "def euler_method(T=10, y0=[0, 0], h=.01, method=2):\n", " \"\"\"\n", " First-order numerical procedure for solving ODE given initial condition.\n", " Parameters:\n", " T: total period (in s) of the numerical integration\n", " y0: initial state [position, velocity]\n", " h: step for the numerical integration\n", " method: Euler method implementation, one of the following:\n", " 1: 'forward' (standard)\n", " 2: 'semi-implicit' (a.k.a., symplectic, Euler–Cromer)\n", " 3: 'semi-implicit variation' (same results as 'semi-implicit')\n", " Two coupled first-order ODEs:\n", " dydt = v\n", " dvdt = a # calculate the expression for acceleration at each step\n", " Two equations to update the values of the variables based on first-order difference:\n", " y[i+1] = y[i] + h*v[i]\n", " v[i+1] = v[i] + h*dvdt[i]\n", " Returns arrays time, [position, velocity]\n", " \"\"\"\n", " N = int(np.ceil(T/h))\n", " y = np.zeros((2, N))\n", " y[:, 0] = y0\n", " t = np.linspace(0, T, N, endpoint=False)\n", " for i in range(N-1):\n", " if method == 1: # forward (standard) Euler method\n", " y[0, i+1] = y[0, i] + h*y[1, i]\n", " y[1, i+1] = y[1, i] + h*dvdt(t[i], y[:, i])\n", " elif method == 2: # semi-implicit Euler (Euler–Cromer) method\n", " y[1, i+1] = y[1, i] + h*dvdt(t[i], y[:, i])\n", " y[0, i+1] = y[0, i] + h*y[1, i+1]\n", " elif method == 3: # variant of semi-implicit (equal results)\n", " y[0, i+1] = y[0, i] + h*y[1, i]\n", " y[1, i+1] = y[1, i] + h*dvdt(t[i], [y[0, i+1], y[1, i]])\n", " else:\n", " raise ValueError('Valid options for method are 1, 2, 3.')\n", "\n", " return t, y\n", "\n", "\n", "def dvdt(t, y):\n", " \"\"\"\n", " Returns dvdt at t given state y.\n", " \"\"\"\n", " d = 0.5 # length of the pendulum in m\n", " g = 10 # acceleration of gravity in m/s2\n", " return -g/d*np.sin(y[0])\n", "\n", "\n", "def plot(t, y, labels): \n", " \"\"\"\n", " Plot data given in t, y, v with labels [title, ylabel@left, ylabel@right]\n", " \"\"\"\n", " fig, ax1 = plt.subplots(1, 1, figsize=(10, 4))\n", " ax1.set_title(labels[0])\n", " ax1.plot(t, y[0, :], 'b', label=' ')\n", " ax1.set_xlabel('Time (s)')\n", " ax1.set_ylabel(u'\\u2014 ' + labels[1], color='b')\n", " ax1.tick_params('y', colors='b')\n", " ax2 = ax1.twinx()\n", " ax2.plot(t, y[1, :], 'r-.', label=' ')\n", " ax2.set_ylabel(u'\\u2014 \\u2027 ' + labels[2], color='r')\n", " ax2.tick_params('y', colors='r') \n", " plt.tight_layout()\n", " plt.show() " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2020-06-14T19:57:55.795017Z", "start_time": "2020-06-14T19:57:55.392588Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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