CSIR Physical Sciences: Questions 388 - 389 of 389

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Passage

In the absence of an applied torque a rigid body with three distances principal moments of inertia given by I1,I2andI3 is rotating freely about a fixed point inside the body. The Euler equations for the components of its angular velocity (ω1,ω2,ω3) are

ω˙1=I2I1I1ω2ω3,ω˙2=(I3I1)I2ω1ω3,ω˙3=I1I2I3ω1ω2 (June)

Question number: 388 (2 of 2 Based on Passage) Show Passage

» Classical Mechanics » Rigid Body Dynamics - Moment of Inertia Tensor

Appeared in Year: 2011

MCQ▾

Question

The constant of motion are –

Choices

Choice (4) Response

a.

I1ω12+I2ω22+I3ω32andω1+ω2+ω3

b.

I1ω12+I2ω22+I3ω32andI12ω12+I22ω22+I32ω32

c.

ω12+ω22+ω32andI1ω1+I2ω2+I3ω3

d.

ω12+ω22+ω32andI12ω12+I22ω22+I32ω32

Passage

Consider the matrix M=(111111111) (June)

Question number: 389 (1 of 1 Based on Passage) Show Passage

» Mathematical Methods of Physics » Taylor & Laurent Series

Appeared in Year: 2011

MCQ▾

Question

The exponential of M simplifies to (I is the 3×3 identity matrix)

Choices

Choice (4) Response

a.

eM=I+33M

b.

eM=I+M+M22!

c.

eM=I+(e313)M

d.

eM=(e1)M

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