tag:blogger.com,1999:blog-8643904148340414752.post8431597899269839095..comments2024-03-06T01:16:35.550-08:00Comments on Physics For Games: True PhysicsEric Brownhttp://www.blogger.com/profile/00315121935974620846noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-8643904148340414752.post-3625214398483189472018-05-25T16:31:08.833-07:002018-05-25T16:31:08.833-07:00This comment has been removed by the author.tonyonhttps://www.blogger.com/profile/08253501266473243514noreply@blogger.comtag:blogger.com,1999:blog-8643904148340414752.post-16070565874284361362018-05-25T16:19:30.548-07:002018-05-25T16:19:30.548-07:00This comment has been removed by the author.tonyonhttps://www.blogger.com/profile/08253501266473243514noreply@blogger.comtag:blogger.com,1999:blog-8643904148340414752.post-61872649519470044222018-05-21T15:14:39.410-07:002018-05-21T15:14:39.410-07:00This comment has been removed by the author.tonyonhttps://www.blogger.com/profile/08253501266473243514noreply@blogger.comtag:blogger.com,1999:blog-8643904148340414752.post-6376372900334954392018-05-21T14:57:40.521-07:002018-05-21T14:57:40.521-07:00This comment has been removed by the author.tonyonhttps://www.blogger.com/profile/08253501266473243514noreply@blogger.comtag:blogger.com,1999:blog-8643904148340414752.post-34843125820170879022010-05-14T19:48:10.130-07:002010-05-14T19:48:10.130-07:00Network systems can be solved using differential e...Network systems can be solved using differential equations and linear algebra. I've seen such systems solved in books on differential equations, or perhaps books on mechanics. If I find a good reference, I'll let you know.<br /><br />I know that linear spring networks are analytically solvable, such as a linear string of point masses connected by springs. Such a system is useful for hair, or ropes, or perhaps articulated limbs of an animated character.<br /><br />To approximate the spring network, you would just solve each spring as if it were independent from the other springs. If the springs all have the same stiffness, it turns out to be a pretty good approximation.Eric Brownhttps://www.blogger.com/profile/00315121935974620846noreply@blogger.comtag:blogger.com,1999:blog-8643904148340414752.post-83285682544053010992010-05-14T15:25:56.727-07:002010-05-14T15:25:56.727-07:00O.K. I understand what you mean now, thanks.
Can ...O.K. I understand what you mean now, thanks.<br /><br />Can I ask another question?<br />In your article in Game Developer you mention how many other types of force functions could be used by solving for an analytical expression describing their acceleration. Some of the examples sound very interesting, but I wonder if you have some reference for how you would develop the analytical expressions? For instance, a network of springs or a multi-jointed rigid body system. Can you really write an expression for such things (even just a double pendulum can be chaotic), or if not, can they be approximated?hellcatshttps://www.blogger.com/profile/08277779415941599788noreply@blogger.comtag:blogger.com,1999:blog-8643904148340414752.post-78270322411271638122010-05-07T08:39:09.406-07:002010-05-07T08:39:09.406-07:00If dv = ∫a dt
then the average of the acceleratio...If dv = ∫a dt<br /><br />then the average of the acceleration over the time interval is <br /><br /><a> = dv / Δt<br /><br />or<br /><br />dv = <a> Δt<br /><br />If you assume that the acceleration is constant over the time interval, and you set this constant value to be equal to the average acceleration, this assumption only affects the value of dx, which becomes<br /><br />dx = 1/2 <a> Δt^2<br /><br />or<br /><br />dx = 1/2 dv Δt<br /><br />In otherwords, I'm not talking about the average of the acceleration evaluated at the two end points, I'm talking about the analytical average of the acceleration across the time interval.Eric Brownhttps://www.blogger.com/profile/00315121935974620846noreply@blogger.comtag:blogger.com,1999:blog-8643904148340414752.post-72089143192653768382010-05-05T21:24:39.038-07:002010-05-05T21:24:39.038-07:00Why do you call your method "average accelera...Why do you call your method "average acceleration" when you are computing acceleration exactly? It seems more like "average velocity" to me. There is another method called "average acceleration" which is a form of Newmark integrator. In that method v1 = v0 + 1/2 (a0 + a1) delta_thellcatshttps://www.blogger.com/profile/08277779415941599788noreply@blogger.com