How to implement 2D rigid body motion?

Question

I'm already depending on two NPM packages for 2D collision and differential equations:

• sat
• rungeKutta

I've a basic simulation structure, but don't know where to start with to use these two packages in my step() forward method that should iterate rigid bodies and their joints:

export default class Simulation {
    /**
     * Global gravity.
     */
    gravity: Vector;

    /**
     * Timestep length during a step.
     */
    timestepLength: number;

    // Contained rigid bodies
    private readonly _bodies: Body[] = [];

    // Joints between rigid bodies
    private readonly _joints: Joint[] = [];

    constructor(options: SimulationOptions) {
        this.gravity = options.gravity;
        this.timestepLength = options.timestepLength === undefined ? 1 / 60 : options.timestepLength;
    }

    step() {
        for (const body of this._bodies) {
            //
        }
    }
}
```