Why is my velocity decaying?

Question

Programming in Java. Tinkering around with physics. My entities all have position and velocity. In the main loop, all I'm doing is applying gravity and bouncing off the edges, like so:

    //  add gravity vector
    o.velocity.add(GRAVITY.cpy().mul(dt));

    //  bounce off walls
    if ((o.position.x<0 && o.velocity.x<0) || (o.position.x>WORLD_SIZE_X && o.velocity.x>0))
        o.velocity.x*=-1;

    //  bounce off of ground
    if (o.position.y<=0.0f) {
        o.position.y=0.0f;
        if (o.velocity.y<0)
            o.velocity.y *= -1;
    }

The x and y values of my vectors are just floats.

For the first second it looks like it's working fine, but the vertical velocities slowly decay. Any idea why?

Answer 1

As long as you only apply constant acceleration (i.e. from constant gravity) Eulers Method is accurate and the ball must bounce forever, reaching its initial position again after each bounce phase. If not, then there is something wrong with the implementation of Euler's Method. Here is how it should look like:

void update(float dt)
{
    position += velocity * dt + acceleration * 0.5 * dt * dt;
    velocity += acceleration * dt;
    // handling only the simple ground collision case here
    if(position.x < radius)
    {
        velocity = -velocity;
    }        
}

Note the acceleration is constant here, its simply the gravity.

EDIT:

It seems both, the article on gaffergames and the code in the question use a simpler form of Euler's Method, namely:

     position += velocity * dt;
     velocity += acceleration * dt;

whereas this one as also shown in this paper:

     position += velocity * dt + acceleration * 0.5 * dt * dt;
     velocity += acceleration * dt;

is still capable of correctly integratiing constant accelerations.

Note: This answer is not supposed to mean that the Euler Method is a good choice for complex physics and non-constant accelerations, nor that you should stick to it once you want to add more physics dynamics to your scene. However, if the application will only use constant acceleration, then this method perfectly fits your needs.

Answer 2

Your objects are bouncing with subsequently smaller bounces because you are applying basic newtonian physics rules to your objects, so they mimic behavior of such objects as you'd expect them to in real life.

You are constantly applying gravity to the velocity of the objects.

When you flip the direction of velocity, the object is now moving up, with an upward velocity, but you are removing some of this velocity with a downward gravity velocity application. With perfect elasticity, and zero friction, you'd expect the object to reach the previous height, but...

You are using Euler integration to approximate the integration of force. This approximation underestimates the effect of the force application.

So when your object hits the ground and velocity is flipped, it can't reach as high as it was before, because the application of gravity is not perfectly accurately integrated (it would be if you had an infintesimally small timestep).

Read "Why Euler's is never good enough": http://gafferongames.com/game-physics/integration-basics/

I think that Euler's actually is often good enough, but that's another matter...

Answer 3

Olhovsky explains the problem, but he left out the simple fix. Apply gravity twice.

Basically you are doing three things over and over.

Gravity
Collision
Movement

Swap the order of any two and you'd actually get the opposite problem. Do a halfway swap and you are even. In practice that means do half the gravity before collision checks, and half the gravity after.

½ Gravity
Collision
½ Gravity
Movement