ElasticCollision2D.java

package com.thealgorithms.physics;

/**
 * 2D Elastic collision between two circular bodies
 * Based on principles of conservation of momentum and kinetic energy.
 *
 * @author [Yash Rajput](https://github.com/the-yash-rajput)
 */
public final class ElasticCollision2D {

    private ElasticCollision2D() {
        throw new AssertionError("No instances. Utility class");
    }

    public static class Body {
        public double x;
        public double y;
        public double vx;
        public double vy;
        public double mass;
        public double radius;

        public Body(double x, double y, double vx, double vy, double mass, double radius) {
            this.x = x;
            this.y = y;
            this.vx = vx;
            this.vy = vy;
            this.mass = mass;
            this.radius = radius;
        }
    }

    /**
     * Resolve instantaneous elastic collision between two circular bodies.
     *
     * @param a first body
     * @param b second body
     */
    public static void resolveCollision(Body a, Body b) {
        double dx = b.x - a.x;
        double dy = b.y - a.y;
        double dist = Math.hypot(dx, dy);

        if (dist == 0) {
            return; // overlapping
        }

        double nx = dx / dist;
        double ny = dy / dist;

        // relative velocity along normal
        double rv = (b.vx - a.vx) * nx + (b.vy - a.vy) * ny;

        if (rv > 0) {
            return; // moving apart
        }

        // impulse with masses
        double m1 = a.mass;
        double m2 = b.mass;

        double j = -(1 + 1.0) * rv / (1.0 / m1 + 1.0 / m2);

        // impulse vector
        double impulseX = j * nx;
        double impulseY = j * ny;

        a.vx -= impulseX / m1;
        a.vy -= impulseY / m1;
        b.vx += impulseX / m2;
        b.vy += impulseY / m2;
    }
}