Bounce Over Time

• Ball Bounce Simulation

elev = degreesToRadians(45); //elevation
v = 2000; //velocity
e = .7; //elasticity
f = .5; //friction
g = 5000; //gravity
nMax = 9; //maximum number of bounces
tLaunch = 0; //launch time

vy = v*Math.sin(elev);
vx = v*Math.cos(elev);
if (time >= tLaunch){
t = time - tLaunch;
tCur = 0;
segDur = 2*vy/g;
tNext = segDur;
d = 0; // x distance traveled
nb = 0; // number of bounces
while (tNext < t && nb <= nMax){
d += vx*segDur;
vy *= e;
vx *= f;
segDur *= e;
tCur = tNext;
tNext += segDur;
nb++
}
if(nb <= nMax){
delta = t - tCur;
x = d + delta*vx;
y = delta*(vy - g*delta/2);
}else{
x = d;
y = 0;
}
value + [x,-y]
}else
value

• Keyframe Bounce

e = .7; //elasticity
g = 5000; //gravity
nMax = 9; //maximum number of bounces

n = 0;
if (numKeys > 0){
n = nearestKey(time).index;
if (key(n).time > time) n--;
}
if (n > 0){
t = time - key(n).time;
v = -velocityAtTime(key(n).time - .001)*e;
vl = length(v);
if (value instanceof Array){
vu = (vl > 0) ? normalize(v) : [0,0,0];
}else{
vu = (v < 0) ? -1 : 1;
}
tCur = 0;
segDur = 2*vl/g;
tNext = segDur;
nb = 1; // number of bounces
while (tNext < t && nb <= nMax){
vl *= e;
segDur *= e;
tCur = tNext;
tNext += segDur;
nb++
}
if(nb <= nMax){
delta = t - tCur;
value + vu*delta*(vl - g*delta/2);
}else{
value
}
}else
value

• Keyframe Overshoot

freq = 3;
decay = 5;
n = 0;
if (numKeys > 0){
n = nearestKey(time).index;
if (key(n).time > time) n--;
}
if (n > 0){
t = time - key(n).time;
amp = velocityAtTime(key(n).time - .001);
w = freq*Math.PI*2;
value + amp*(Math.sin(t*w)/Math.exp(decay*t)/w);
}else
value

REF: Motionscript.com bounce-and-overshoot


veloc = 20; 

amplitude = 10; 

decay = .8; 

y = amplitude*Math.cos(veloc*time)/Math.exp(decay*time);

value + [0,y]