# Double Accumulator Math -Proof and Error

1. May 21, 2012

### mue103

I'm working on a double accumulator math problem at work and I keep stuff. I need to calculate the position of an object overtime, when given the acceleration, initial distance, upper and lower velocity limits (triangle wave velocity).

My first issues is associated with the distance equation: distance = xo + vo*t+(.5*a*t*t)

Example in excel....
a = 67108850 m/s2
vo = 0 m/s
x0 = 0 m

Time X(should be) X(formula)
0 0 0
1 335544320 335544320
2 603979790 134217700
3 8053006410 301989825
4 939524180 536870800

As you ca see the distance formula does not what the "should be" values are. If I modify the distance formula to be: d = x0 + v0*t+(.5*a*t*t)-(.5*a*t). Everything works.... Why is that?

Next issue is the ramping up and ramping down issue with the velocity. The number match when ramping up or down, but do not match when it makes the transition up or down.

Example in excel.... (Triangle wave)
a = 67108850 m/s2
vo = 0 m/s
x0 = 0 m

Time X(should be) X(formula)
0 0 0
1 335544320 335544320
2 603979790 603979790
3 8053006410 8053006410
4 939524180 939524180
5 1006633100 1006633100
6 1006633170 1006633170
7 1073742090 939524390
8 1207959860 805306760
9 1409286480 335544950

The numbers match on the ramping up section (0 to 6 section), but do not on the ramp down. Any suggestions?

Thanks