Inertia Tensor
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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 ...
Chapter 12. Rotation of a Rigid Body - Physics & Astronomy
physics.gsu.eduC. Tensor Product D. Cross Product E. Angular Product. Moment of inertia is A. the rotational equivalent of mass. ... Here the quantity I is called the object’s moment of inertia. The units of moment of inertia are kg m 2. An object’s moment of inertia depends on the axis of rotation.
Lecture 2 - Shear and Bending Moment and Review of Stress
me.utep.eduly ad Iz are the second-moment Of inertia with respect to and +z axes (see Appendix 18) (y, z) is the location where the normal bending stress is to be calculated. It ... Add the stresses together into a Stress Tensor . Remember to draw the Stress Distribution Diagrams I st This informs the location on the cross-section where the stress are
Lecture 2: The Navier-Stokes Equations - Harvard University
projects.iq.harvard.eduux of momentum is a second order tensor, which makes the book-keeping more cumbersome, because there are several contributions to the momentum budget, namely: i) Inertial terms due to the motion of the uid across the faces of cube, ii) pressure terms due to the component of the contact force normal to
Tensor Calculus - Saint Mary's University
www.ap.smu.caquantities (e.g., moment of inertia, viscosity, spin) and in the senior year, Riemannian ge- ... basis of tensor calculus, and the subject of this primer. 1Examples of tensors the reader is already familiar with include scalars (rank 0 tensors) and vectors (rank 1 tensors).