An Introduction to Advanced Dynamics
S.W. McCuskeyChapter
I. Fundamentals of Newtonian Dynamics ........................ 1
1-1Kinematical preliminaries ............................. 1
1-2Mass and force ........................................ 3
1-3Newton’s laws of motion . ............................. 5
1-4Moment of a force ; angular momentum .................. 9
1-5Newton’s Second Law applied to rotational motion . . . 10
1-6Work and energy .......................................11
1-7Conservative force fields .............................12
1-8Conservation laws .....................................14
1-9Energy diagrams . .....................................15
1-10Impulsive motion ......................................18
1-11Impact and collision ........................ 20
1-12Systems of particles ..................................22
1-13The energy of a particle system .......................26
1-14Motion in a moving reference frame ....................28
1- 15Motion on the rotating earth ........................ 33
Chapter 2. Hamilton’s Principle and Lagrange’s Equations . . 43
2-1 The principle of virtual work ...........................43
2-2 D’Alembert’s principle ..................................47
2-3 Variational principles ..................................49
2-4 Hamilton’s principle ....................................51
2-5 Generalized coordinates .................................54
2—6 Lagrange’s equations ....................................55
2-7 Nonholonomic and nonconservative systems . ..............62
2-8 Impulsive motion . ......................................66
2-9 Relativistic dynamics ...................................69
Chapter 3. Central Force Motion .............................79
3-1 General properties of central force motion ..............79
3-2 Inverse square forces ...................................85
3-3 Stability of circular orbits ............................90
3-4 Repulsive forces: scattering ............................95
3-5 The virial theorem .....................................102
Chapter 4. Dynamics of a Rigid Body ........................108
4-1 Rigid-body motion ......................................108
4-2 Moments and products of inertia. . .....................111
4-3 Computation of inertial moments ........................113
4-4 Principal axes .........................................115
4-5 Euler’s equations of motion ............................120
4-6 Rotational kinetic energy of a rigid body . . . . . . . 124
4-7Euler's angles .................................................125
4-8Motion of a torque-free system .................................129
4-9The motion of a top under gravity ..............................134
4-10Motion of a spinning projectile . . ............................139
4-11Motion of a rocket .............................................144
Chapter 5. Oscillatory Motion ..........................................155
5-1 The equations of motion ...........................................155
5-2 An example: two statically coupled masses ..........................158
5-3 Orthogonality and normalizing conditions ...........................160
5-4 Normal coordinates .................................................164
5-5 An example of dynamic coupling .................................... 169
5-6 Forced oscillations ................................................170
5-7 Nonconservative systems ............................................173
5-8 Stability of oscillatory motion ....................................182
5-9 The vibrating string . ............................................188
Chapter 6. Hamilton's Equations and Phase Space ........................ 204
6-1 Hamilton's equations ....................................................................... 201
6-2 An example: electron in motion ...................................................... 207
6-3 Ignorable or cyclic coordinates ...................................................... 208
6-4 Phase space .................................... 213
6-5 Lionville’s theorem . 215
6-6 Phase plane analysis .............................. . .............................. 218
6-7 Nonlinear oscillatory motion . . . . . . . . . . . 221
6- 8 Stability of periodic motion .................................... 225
Chapter 7. The Hamilton- J a coni Equation .......................................... 233
7- 1 Canonical transformations ............................................................ 233
7-2 The Hamilton-Jacobi equation ...................................................... 236
7-3 Action and angle variables . . . . . . . . . . . 246
References
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255
Index
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257