Search results with tag "Inertia tensor"
3D Rigid Body Dynamics: The Inertia Tensor
ocw.mit.eduG] is the tensor of inertia (written in matrix form) about the center of mass G and with respect to the xyz axes. The tensor of inertia gives us an idea about how the mass is distributed in a rigid body. Analogously, we can define the tensor of inertia about point O, by writing equation(4) in matrix form. Thus, we have H O = [I O] ω ,
Lecture 34: Principal Axes of Inertia
www.physics.arizona.eduLecture 34: Principal Axes of Inertia • We’ve spent the last few lectures deriving the general expressions for L and Trot in terms of the inertia tensor • Both expressions would be a great deal simpler if the inertia tensor was diagonal. That is, if: or • Then we could write Iij =Iiδij 1 2 3 0 0 0 0 0 0 I I I = I 2 rot, , 1 1 1 2 2 2 i ...
3. The Motion of Rigid Bodies - DAMTP | Department of ...
www.damtp.cam.ac.uk3.2 The Inertia Tensor Let’s look at the kinetic energy for a rotating body. We can write T = 1 2 X i m ir˙2 i = 1 2 X i m i (! ⇥r i)·(! ⇥r i) = 1 2 X i m i (! ·!)(r i ·r i)(r i ·!)2 (3.17) Or, in other words, we can write the kinetic energy of a rotating body as T = 1 2! aI ab! b (3.18) where I ab, a,b =1,2 ...