Converted from https://docs.google.com/document/d/1VkgliXVgtcaJZGhttjZvOVLT_xxm9XTmXL06JTQOKRo

BackwardEulerController.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class BackwardEulerController : MonoBehaviour
{
    public float gain = 200; //200-700;
    public float damp = 20; //20-100;

    public Transform target = null;

    Vector3 velocity = Vector3.zero;

    void Update()
    {
        transform.position = Integrate(target.position,transform.position, ref velocity,gain,damp, Time.deltaTime);
    }

    static public Vector3 Integrate(Vector3 target, Vector3 current, ref Vector3 velocity, float gain, float damp, float dt)
    {
        float g = damp * dt + gain * dt * dt;
        g = 1.0f / (1.0f + g);
        float _gain = gain * g;
        float _damp = (damp + gain * dt) * g;
        Vector3 diff = target - current;
        Vector3 force = diff * _gain - velocity * _damp;
        velocity += velocity + force * dt;
        return current + velocity * dt;
    }
}