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Forces and time

Started by yarniso Apr 27, 2004 at 3:24 AM 4 replies 1.2k views

Original Post

Apr 27, 2004 at 3:24 AM

Hi all, I am trying to implement a rigid body dynamics simulator. While implementing a simple canon I was wondering about this: Say that I apply a force Fblast to the projectile for 25ms, but I use a timestep of 100ms. If I don''t do anything about this time difference, I will calculate the path of the projectile given a force Fblast for 100ms. But I have a feeling that I can''t just say that Fblast for 25ms = Fblast/4 for 100ms. How can you solve this. Decreasing the timestep is a solution, but are there any other solutions? Kind regards, Bart

oliii

Apr 27, 2004 at 3:44 AM

what you are describing is a change in momentum, or an impulse. A force applied over time.

the change in momentum is

m * dV = Impulse = Force * dt

m : mass
dV : change in velocity
dt : delta time (25 ms)
Force : force applied other delta time

so, the change in velocity after the impulse is applied becomes

dV = (Force * dt) / m

the velocity after the force is applied is then simply

V = V + dV

yarniso

Apr 27, 2004 at 4:05 AM

Ah, very clear. Thank you

shadow12345

Apr 27, 2004 at 10:47 AM

How to you know what the applied force is when you have two objects with arbitrary velocities and masses and they collide? For instance, I'm shooting a ball, it bounces around the world and then collides with the player. I've decomposed the velocities into components normal to the collision plane, I've got coefficients for restitution(it's just perfectly elastic for ease of implementation right now), equations for impulse, but I have no clue what the applied impulse should be. Is it just the mass * velocity of one of the objects?

EDIT:
ack, I'm realizing this is more involved than I thought. i've got the equations, and to be honest you've told me enough, I'm just trying to figure out why the equations work and get a feel for what they really mean.

[edited by - shadow12345 on April 27, 2004 1:15:25 PM]

shadow12345

Apr 29, 2004 at 7:10 PM

and how do you know acceleration? That's just the problem with this scenario:

you don't know the impulse 'force' and the new velocity at the same time, so you can't solve for the new position. You've got to solve for the impulse force using the coefficient of restitution equations, then calculate the new velocity (the 'acceleration') and then calculate the new position.

and what I asked earlier was this:
is the impulse equation the limit of the force equation as deltat approaches zero?

force = ma

impulse = mass * (v+ - v-)

acceleration = (vfinal - finitial) / deltaT

v+ = velocity after collision (unknown)
v- = velocity before collision

impulse force is also unknown when two arbitrary objects collide with an arbitrary velocity

[edited by - shadow12345 on April 29, 2004 8:11:06 PM]

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