|Jul22-04, 04:48 AM||#1|
Dynamics of a free hanging 3D needle
Hi! I would be extremely grateful if anyone could help me figure out this mess... I hadn't touched mechanics for too many years and I guessed i gotten myself a little confused...
I am trying to model a 3D needle/object in a virtual world... I have done the part on freebodies collision... but i think i am starting to get everything mixed up...
I am now trying to model a free hanging needle which hangs from a thread, and the needle is suppose to response to other objects. What i did previously was a zero gee free body needle, which can be manipulated by other objects...
now with addition of gravity and a reaction force from a thread confused me, because in the prev part, I made use of impulses to calculate and model the resultant responses... What i did was to just compute the resultant orientation and position of the needle, with respect to its center of mass, as in i pretend the needle is a point mass.
So now the problem I am facing is tat, for a free hanging needle in an initially unstable elevated level, the resultant force at the CM is 0, and I can get the resultant moment. I can calculate the position of the CM in the next time step, by finding the acceleration at CM, but I have no idea how can i compute the orientation of the needle at the next time step???
Summation of Moments = Moment of Inertia x alpha
so i can find:
Angular velocity = initial angular velocity + alpha
??? so assuming i am rite,
how can i integrate this with impulses? as in a object hitting the free hanging needle...
cuz for my free body collision,
Angular velocity = inverse of moment of inertia x angular momentum
so which one shld i use to find the angular velocity of the needle so tat i can compute its orientation in the next time step??
|Jul22-04, 09:03 AM||#2|
This is only a suggestion -- try thinking of the needle as a two point linked mass problem ( in reallity it is distributed ), this may indicate what the steps are , there is not enough info at one point since the fields differ at different points thru' the needle length. In this simplified model there are only two restrictions to apply the max thread length ( it may not be taut) and the rigid point to point link .This is a small time step approach in that you do not have to explicitly deal with rotation just the point movements under forces.
I have done this for 2D using 4 points with rubber band connections without any major problems.
|Jul22-04, 11:33 AM||#3|
I thought it through a little , but do not take for granted. Start with two point mass in a hanging state with the thread taut. The thread is attached to A.
For small time step dt , calc the force on A hence the accelleration and direction , if the direction is such that the thread remains taut calculate the radial velocity and v= v+ a.dt in whatever direction and d = d + v.dt , if the thread goes loose calc the appropriate movement.
Assume this movement is communicated to B via the CM of the system to obtain new x,y,z of B.
Then switch to B calc from forces it's movement in dt . Assume communicated to A via the CM , apply the same reasoning concerning thread tautness.
Keep iterating around this loop. I'm pretty sure that for a free needle this could work , I'm not sure about the thread reaction situation , but what I am doing is to imagine a real situation in which there is a finite time for the masses to communicate and what happens then.
The rubber banding I mentioned solves this problem and you can choose a law which simulates rigidity , unfortunately I've lossed the software and cannot remember all the details. Ray.
|Jul23-04, 02:37 AM||#4|
Dynamics of a free hanging 3D needle
hmmm i dun quite get what u mean...
lemme think on it awhile...
i can't do it in a normal way, cuz I am writing a program to do the simulation at real time, so I am pretty much constrained in how i represent my model...
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