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Cross product is a mathematical convention where X, Y and Z are concerned
Given one conventional definition for the crossproduct x, we have
X = Y x Z
Y = Z x X
Z = X x Y
Drawing axes is also another convention, a pictorial one. If you use the crossproduct convention above (purely mathematical) with a pictorial convention similar to DirectX (the coordinate system is stated with y upwards,
2005-04-17 23:56:48 UTC in mjbWorld
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Update:
I should NOT have posted : Modulus of W is (97%) constant
After, more simulations were done with a wider range of input data, it was found that modulus of W varied by a great magnitude while an object is spining freely.
At this point, I can't run a simulation accurately enough to say that the modulus is constant, or a variable, for a freely rotating object.
Before, integrating...
2005-04-02 05:56:25 UTC in mjbWorld
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Update:
*Coriolis and centripetal forces are present in the object and these cause the change in the direction of W
*Modulus of W is (97%) constant
*Euler's equations hold for the local frame of the object (when I used the small numerical change in W for the current frame during the time step)
*A numerical simulation would be just as fast as a theoretical calculation for obtaining the new...
2005-03-14 01:41:37 UTC in mjbWorld
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Update:
According to my simulation of many arbituary free rotationg body :)
The rate of change of W_global is NOT constant
The rate of change of W_local is NOT constant
W_global is NOT constant
W_local is NOT constant
However euler's equations hold
dWx/dt = Wy*Wz*(Iy - Iz) / Ix
dWy/dt = Wz*Wx*(Iz - Ix) / Iy
dWz/dt = Wx*Wy*(Ix - Iy) / Iz
where dW/dt and W are both measured from the...
2005-03-03 22:15:14 UTC in mjbWorld
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Tx = wy.wz.Iz − wy.wz.Iy + (dwx/dt)Ix
Ty = wx.wz.Ix − wx.wz.Iz + (dwx/dt)Ix
Tz = wx.wy.Iy − wx.wy.Ix + (dwz/dt)Iz
The Euler's equations can be found on this pdf
http://online.redwoods.cc.ca.us/instruct/darnold/deproj/sp03/dfrank/depresentation.pdf
Further reading on this page.
http://theory.ph.man.ac.uk/~mikeb/lecture/pc167/rigidbody/stability.html.
2005-02-28 19:04:04 UTC in mjbWorld
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I did some revision on
http://www.gamedev.net/community/forums/topic.asp?topic_id=254716&forum_id=20
It deals with the actual motion that a freely rotating body has.
(1)Angular momentum vector in the global frame is always constant.
(2)Rotational energy is always constant
I repeated the simulation using the equation
R * ( Ilocla^(-1) * ( R^(-1) * L ) ) = W
where R is the...
2005-02-28 17:19:38 UTC in mjbWorld
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I will email u a bitmap of the conventions used and a diagram of the Force and Position the day after tomorrow. I will be away tomorrow.
Crossproduct operation:
I think
X = Y x Z
Y = Z x X
Z = X x Y
This is just one mathematical convention for the operation
Rotation convention:
I think
Wx means the rotation 90 degree arc from +Z to +Y
Wy means the rotation 90 degree arc from +X to...
2005-02-18 01:03:37 UTC in mjbWorld
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Approaching velocity = 36.0229025579962
Energy before = 7310.5151984483746
Energy after = 7310.5151984483746
Using the global axes
The objects characteristics:
Masses of objects A and B
Ma = 4.3900000000000
Mb = 12.2100000000000
Inertia about principal axes for objects A and B
Ia = 11.9400000000000, 11.1300000000000, 5.7.
2005-02-17 22:13:33 UTC in mjbWorld
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Oh I left out R and N, I will adjust the program to display R and N. I will do this now.
N is in the direction of B to A's surface, and R is a vector from the center of mass to the point of the collision on the surface.
I will try making a bitmap diagram.
2005-02-17 21:54:42 UTC in mjbWorld
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Wow! I just realised that this was the result that was originally posted by Martin.
Quote "
I think its linear motion is simple, since F = ma = m dv/dt this gives:
Change in velocity = dv = (F/m) dt = impulse/m
So the linear motion will be in the same direction as the impulse, even if the impulse is applied at a point offset from the centre of mass, this seems counter intuitive and...
2005-02-17 17:10:44 UTC in mjbWorld
