Analytical Mechanics Of Aerospace Systems-02--Schaub-p571--Pirx.pdf

ANALYTICAL MECHANICS
of
AEROSPACE SYSTEMS
Hanspeter Schaub
and
John L. Junkins
January 1, 2002
Contents
Preface ix
I BASIC MECHANICS 1
1 Particle Kinematics 3
.................... 3
BasicGeometry........................ 3
Cylindrical and Spherical Coordinate Systems . . . . . . . 6
........................ 8
Angular Velocity Vector . . . . . . . . . . . . . . . . . . . 8
Rotation about a Fixed Axis . . . . . . . . . . . . . . . . 10
TransportTheorem..................... 11
Particle Kinematics with Moving Frames . . . . . . . . . 15
2 Newtonian Mechanics 25
’sLaws............................ 25
....................... 29
Constant Force . . . . . . . . . . . . . . . . . . . . . . . . 29
Time-VaryingForce..................... 32
icEnergy........................ 34
LinearMomentum...................... 35
AngularMomentum..................... 35
Dynamics of a System of Particles . . . . . . . . . . . . . . . . . 38
Equations of Motion . . . . . . . . . . . . . . . . . . . . . 38
icEnergy........................ 41
LinearMomentum...................... 43
AngularMomentum..................... 45
................. 47
EquationsofMotion..................... 47
icEnergy........................ 49
LinearMomentum...................... 50
AngularMomentum..................... 51
......................... 52
iii
iv CONTENTS
3 Rigid Body Kinematics 63
....................... 64
............................. 70
...................... 78
........................... 85
................... 91
Modified Rodrigues Parameters . . . . . . . . . .