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Question by Maxter · Sep 16, 2015 at 12:33 PM · physics2dpathtrajectorypredictionconstant force

2D Trajectory prediction in open space

I want to draw a line (I have Vectrocity) that shows predicted trajectory of an object based on acting forces (a single force to begin with).

Force is applied by this script:

 using UnityEngine;
 using System.Collections;
 
 public class AccelerateToPoint : MonoBehaviour
 {
 
     Rigidbody2D body;
     Transform myTransform;
 
     public float acceleration = 100;
 
     private float startTime;
     private bool move = false;
     private Vector3 targetPosition;
 
     // Use this for initialization
     void Start()
     {
         body = GetComponent<Rigidbody2D>();
         myTransform = transform;
     }
 
     // Update is called once per frame
     void FixedUpdate()
     {
         if (Input.GetMouseButtonDown(0)) {
             // Acquire destination point
             Vector3 pointer = Input.mousePosition;
             targetPosition = Camera.main.ScreenToWorldPoint(pointer);
             targetPosition.z = 0;
             move = true;
         }
         if (move) {
             Vector3 directionToTarget = (targetPosition - myTransform.position).normalized;
             // if target was changed mid-flight we have to find our velocity to the new target
             Vector3 velocityProjectionToTarget = Vector3.Project(body.velocity, directionToTarget);
             float q = velocityProjectionToTarget.normalized == directionToTarget ? 1 : -1;
 
             float S = (targetPosition - myTransform.position).magnitude;
             float t = Mathf.Sqrt(S * 2 / acceleration);
             // this is how much velocity we can reduce to zero on the way to our destination
             float V = acceleration * t;
             // this is our velocity to the target in a very near future
             float velocityThreshold = velocityProjectionToTarget.magnitude * q + (acceleration * Time.fixedDeltaTime * 2);
 
 
 
             bool accelerating;
             Vector3 forceDirection;
             if (V > velocityThreshold) {
                 // if we can reduce more velocity than we have, we will accelerate
                 accelerating = true;
                 forceDirection = directionToTarget;
             } else {
                 // otherwise we will decelerate
                 forceDirection = -directionToTarget;
                 accelerating = false;
             }
 
             // condition to stop the movement:
             // if we decelerate and we almost stopped - stop completely
             if (body.velocity.magnitude < 10 && !accelerating) {
                 myTransform.position = targetPosition;
                 body.velocity = Vector3.zero;
                 move = false;
                 return;
             }
 
             body.AddForce(forceDirection * acceleration);
 
             Debug.Log(
                  string.Format(
                      "t = {0} s; S = {1} m; V = {2} m/s; curV = {3}; {4}",
                      t, S, V, velocityProjectionToTarget.magnitude, accelerating
                  )
             );
         }
     }
 }

If we just click and wait, object travels a straight line and stops at the destination. However, if we change destination mid-flight, object starts orbiting around the destination point (orbit is usually elliptic and this ellipse usually rotates around destination point).

How to predict the motion?

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Answer by Maxter · Sep 18, 2015 at 07:07 PM

I found my solution. You'll need a bit of advanced maths.

These links provided all the necessary information to do what I need: http://gafferongames.com/game-physics/integration-basics/ http://gafferongames.com/game-physics/physics-in-3d/

Algorithm described there is not demanding and it provides pretty accurate predictions.

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