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Question by vitokvachadze_unity · Jan 11, 2020 at 12:25 PM · transform.position

Animating a pendulum by using equation of motion

I want to animate a simple pendulum by using differential equation of motion in Unity3D

alt text

There is a coding challenge video to simulate a "double pendulum" in Processing (Java) by using differential equations for double pendulum.

The idea behind the code is following :

If a function gives the position of something as a function of time, the first derivative gives its velocity, and the second derivative gives its acceleration

Or

Velocity is defined as the rate of change of displacement with respect to time, and acceleration is defined as the rate of change of velocity with respect to time.

I tried to write a similar code in c# for a single pendulum, but there is a weird motion of Bob.

     using System.Collections;
     using System.Collections.Generic;
     using UnityEngine;
 
     public class Pend : MonoBehaviour
     {
      public float theta = 90;
      public float g = 10;
      public float l = 10;
      public float theta_velocity;
      public float theta_acceleration;
      public GameObject ball;
      float alpha = 0;
 
      void Update()
      {
       //equation of motion
       theta_acceleration = -(g/l)*Mathf.Sin(theta);
 
       //I don't fully understand that part of code  
       theta_velocity += theta_acceleration;
       alpha += theta_velocity;
 
         //motion on the circle
         float x = l * Mathf.Sin(alpha);
         float y = l * Mathf.Cos(alpha);
         ball.transform.position = new Vector2(x,y);
      }
     }


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