RE: [Algorithms] Re: Cumalative rotation
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From: Tony C. <to...@mi...> - 2003-04-23 16:04:24
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You probably want to represent both angular momentum and angular velocity separately. They are not guaranteed to be parallel (unlike linear motion). The relationship is: LinearMomentum =3D Mass * LinearVelocity AngularMomentum =3D InertiaTensor * AngularVelocity In the second case, if the inertia tensor is not a multiple of the identity matrix, the two vectors need not be parallel. The conserved quantity is momentum, not velocity. So in the case of angular motion, the angular velocity can change even when no force/torque is applied, because the inertia tensor is fixed in object space, but the object is spinning so it changes in world space (you apply the 'tensor transform' operation to convert it). That's how you get procession and all that good stuff happening. Eventually, a freely spinning object will settle to spinning around one the principle axes of rotation of the object - which are the eigenvectors of the inertia tensor. Tony Cox - Development Lead, Hockey Microsoft Game Studios - Sports -----Original Message----- From: gda...@li... [mailto:gda...@li...] On Behalf Of Tom Forsyth Sent: Wednesday, April 23, 2003 2:26 AM To: gda...@li... Subject: RE: [Algorithms] Re: Cumalative rotation Spin can be represented as a vector - the vector's direction is the axis of spin, the length is the size of the spin. All the usual linear mechanics stuff has a direct and fairly obvious relative in spin dynamics. Velocity->spin. Force->torque. Mass->inertial tensor. etc. Most decent mechanics textbooks should go through the details. Tom Forsyth - Muckyfoot bloke and Microsoft MVP. This email is the product of your deranged imagination, and does not in any way imply existence of the author. |