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Chapter 10: Q5P (page 508)

Point masses 1 at (1, 1, 1) and at (-1, 1, 1).

Short Answer

Expert verified

Answer:

Inertia tensor is t=40004-20-24.

Step by step solution

01

Given Information

The given information is mentioned below:

m1=m2=1r1=1,1,1r2=-1,1,1

02

Definition of Inertia tensor.

Inertia tensor is the angular momentum of a rigid body determined by the product of its tensor and its rotation vector.

03

Find the eigenvalues.

Solve for eigenvalues.

lij=3未ij-1+3未ij--1未1l+未1ll=2-1-1-12-1-1-12+21112-11-12=40004-20-24

04

Find principal axes and corresponding moment of inertia.

Find the moment of inertia.

V1=1,0,0V2=0,-1,1V3=0,1,1

Simplify Further

l1=4l2=6l3=2

Hence, the inertia tensor is, t=40004-20-24.

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