Potential floating point issue with cosine acceleration curve

Question

I am using a cosine curve to apply a force on an object between the range [0, pi]. By my calculations, that should give me a sine curve for the velocity which, at t=pi/2 should have a velocity of 1.0f

However, for the simplest of examples, I get a top speed of 0.753.

Now if this is a floating point issue, that is fine, but that is a very significant error so I am having trouble accepting that it is (and if it is, why is there such a huge error computing these values).

Some code:

// the function that gives the force to apply (totalTime = pi, maxForce = 1.0 in this example)
return ((Mathf.Cos(time * (Mathf.PI / totalTime)) * maxForce));


// the engine stores this value and in the next fixed update applies it to the rigidbody
// the mass is 1 so isn't affecting the result
engine.ApplyAccelerateForce(applyingForce * ship.rigidbody2D.mass);

Update

There is no gravity being applied to the object, no other objects in the world for it to interact with and no drag. I'm also using a RigidBody2D so the object is only moving on the plane.

Update 2

Ok have tried a super simple example and I get the result I am expecting so there must be something in my code. Will update once I have isolated what is different.

For the record, super simple code:

float forceThisFrame;
float startTime;

// Use this for initialization
void Start () {
    forceThisFrame = 0.0f;
    startTime = Time.fixedTime;
}

// Update is called once per frame
void Update () {
    float time = Time.fixedTime - startTime;

    if(time <= Mathf.PI)
    {

        forceThisFrame = Mathf.Cos (time);

        if(time >= (Mathf.PI /2.0f)- 0.01f && time <= (Mathf.PI /2.0f) + 0.01f)
        {
            print ("Speed: " + rigidbody2D.velocity);
        }
    }
    else
    {
        forceThisFrame = 0.0f;
    }
}

void FixedUpdate()
{
    rigidbody2D.AddForce(forceThisFrame * Vector2.up);
}

Update 3

I have changed my original code to match the above example as near as I can (remaining differences listed below) and I still get the discrepancy.

Here are my results of velocity against time. Neither of them make sense to me, with a constant force of 1N, that should result in a linear velocity function v(t) = t but that isn't quite what is produced by either example.

Remaining differences:

The code that is "calculating" the force (now just returning 1) is being run via a non-unity DLL, though the code itself resides within a Unity DLL (can explain more but can't believe this is relevant!)
The behaviour that is applying the force to the rigid body is a separate behaviour.
~~One is moving a cube in an empty enviroment, the other is moving a Model3D and there is a plane nearby~~ - tried a cube with same code in broken project, same problem

Other than that, I can't see any difference and I certainly can't see why any of those things would affect it. They both apply a force of 1 on an object every fixed update.

Potential floating point issue with cosine acceleration curve

2 Answers