EngineeringDynamics

JERRY GINSBERGGeorgia Institute of Technology

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Chapter 1, Page 1

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% Exercise 1.3: Vector calculationsclear allomega = [-50 0 -20]';alpha = [1500 -500 1000]';I = [[500 0 200]; [0 800 0]; [200 0 300]];H = I * omega;partial_H = I * alpha;S = 0.5 * alpha' * partial_H + alpha' * (cross(omega, H));disp(['S = ', num2str(S)])

----S = 1222500000

ω

50−

0

20−

⎛⎜⎜⎝

⎞⎟⎟⎠

:= α

1500

500−

1000

⎛⎜⎜⎝

⎞⎟⎟⎠

:=

Ixx 500:= Iyy 800:= Izz 300:= Ixz 200−:=

I

Ixx

0

Ixz−

0

Iyy

0

Ixz−

0

Izz

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

:= HA I ω⋅

2.900000− 104×

0.000000

1.600000− 104×

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

=:=

partial_HA I α⋅

9.500000 105×

4.000000− 105×

6.000000 105×

⎛⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎠

=:= ω HA×

0.000000

2.200000− 105×

0.000000

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

=

S12

αT⋅ partial_HA⋅ α

Tω HA×( )⋅+ 1.222500 109×=:=

Chapter 1, Page 4

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Chapter 1, Page 5

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Chapter 1, Page 8

Chapter 1, Page 9

Chapter 1, Page 10

Chapter 1, Page 11