create an animated two link manipulator using lagrangian mechanics for link and motor side dynamics in javascript

index.tsx
// Here is an outline of how you can create an animated two-link manipulator using Lagrangian mechanics for link and motor side dynamics in JavaScript:

// Define the constants for the manipulator
const g = 9.81; // gravitational acceleration
const m1 = 1; // mass of link 1
const m2 = 1; // mass of link 2
const l1 = 1; // length of link 1
const l2 = 1; // length of link 2

// Define the Lagrangian function
function lagrangian(th1, th2, dth1, dth2) {
    // Kinetic energy of link 1
    const T1 = 0.5 * m1 * (l1 * dth1) ** 2;
    // Kinetic energy of link 2
    const T2 = 0.5 * m2 * ((l1 * dth1) ** 2 + (l2 * dth2) ** 2 + 2 * l1 * l2 * dth1 * dth2 * Math.cos(th1 - th2));
    // Potential energy of link 1
    const V1 = -m1 * g * l1 * Math.cos(th1);
    // Potential energy of link 2
    const V2 = -m2 * g * (l1 * Math.cos(th1) + l2 * Math.cos(th2));
    // Total Lagrangian
    return T1 + T2 - V1 - V2;
}

// Use a numerical method like Euler's method to simulate the dynamics of the manipulator

// Initialize the state variables (positions and velocities)
let th1 = Math.PI / 4;
let th2 = -Math.PI / 4;
let dth1 = 0;
let dth2 = 0;

// Time step
const dt = 0.01;

// Simulate the dynamics
for (let t = 0; t < 10; t += dt) {
    // Calculate the forces (using Lagrange's equations)

    // Update the velocities and positions using Euler's method

    // Animate the manipulator using a library like p5.js or Three.js
}
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