Multiplication by time step in Sequential Impulses
Posted: Thu Jan 03, 2013 10:11 am
Hello,
I am studying the Sequential Impulse theory for rigid bodies simulation using the slides of Erin Catto from GDC 2009. At the slide 52, it is written that the impulse P is equal to the Force F times the time step h :
P = h F
with the force :
F = J^T lambda
Then, at slide 53, it is written that we have tu update the velocity V2 using the impulse P:
V2 = V2 + M^-1 P
Therefore, according to this equation, the velocity update should be :
V2 = V2 + M^-1 h J^T lambda
However, at slide 56, we see that the velocity update is :
V2 = V2 + M^-1 P
with P = J^T lambda
As you can see here, the multiplication by the time step h has disapeared in the last equation. I have also taken a look at the code of the sequential impulse solver in Box2D and it also seem that we never multiply the force by the time step h to compute the impulse P that we use to update the velocity V2.
There is probably something that I don't understand here but I don't see how we can remove the multiplication by the time step h to compute the impulse P. Does someone has any idea how we can drop this multiplication ?
I am studying the Sequential Impulse theory for rigid bodies simulation using the slides of Erin Catto from GDC 2009. At the slide 52, it is written that the impulse P is equal to the Force F times the time step h :
P = h F
with the force :
F = J^T lambda
Then, at slide 53, it is written that we have tu update the velocity V2 using the impulse P:
V2 = V2 + M^-1 P
Therefore, according to this equation, the velocity update should be :
V2 = V2 + M^-1 h J^T lambda
However, at slide 56, we see that the velocity update is :
V2 = V2 + M^-1 P
with P = J^T lambda
As you can see here, the multiplication by the time step h has disapeared in the last equation. I have also taken a look at the code of the sequential impulse solver in Box2D and it also seem that we never multiply the force by the time step h to compute the impulse P that we use to update the velocity V2.
There is probably something that I don't understand here but I don't see how we can remove the multiplication by the time step h to compute the impulse P. Does someone has any idea how we can drop this multiplication ?