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Introduction to Analytical Mechanics [Kõva köide]

  • Formaat: Hardback, 294 pages, kõrgus x laius: 240x160 mm, kaal: 600 g
  • Ilmumisaeg: 30-Jan-2011
  • Kirjastus: Alpha Science International Ltd
  • ISBN-10: 1842656686
  • ISBN-13: 9781842656686
Teised raamatud teemal:
Introduction to Analytical MechanicsSuurem pilt
  • Formaat: Hardback, 294 pages, kõrgus x laius: 240x160 mm, kaal: 600 g
  • Ilmumisaeg: 30-Jan-2011
  • Kirjastus: Alpha Science International Ltd
  • ISBN-10: 1842656686
  • ISBN-13: 9781842656686
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781842656686.html
This book is an attempt to introduce the modern treatment of classical mechanics so that transition to many fields in physics can be made with the least difficulty. This book deals with the formulation of Newtonian mechanics, Lagrangian dynamics, conservation laws relating to symmetries, Hamiltonian dynamics Hamilton's principle, Poisson brackets, canonical transformations which are invaluable in formulating the quantum mechanics and Hamilton-Jacobi equation which provides the transition to wave mechanics.

Deals with the formulation of Newtonian mechanics, Lagrangian dynamics, conservation laws relating to symmetries, Hamiltonian dynamics Hamilton's principle, Poisson brackets, canonical transformations which are invaluable in formulating the quantum mechanics and Hamilton-Jacobi equation which provides the transition to wave mechanics.
Preface v
1 Fundamentals of Newtonian Mechanics
1(46)
1.1 Axiomatic Foundation of Dynamics
1(2)
1.2 Newton's Laws of Motion 3
First Law
3(2)
Second Law
5(2)
Galilean Principle of Relativity
7(1)
Third Law
8(2)
1.3 Uniform Constant Force Field
10(2)
Falling Objects
10(2)
1.4 Motion in Resisting Mediums
12(4)
Frictional Forces
13(1)
Viscous Forces
14(2)
1.5 Principle of Work and Energy
16(9)
Power
17(2)
Conservative Forces
19(2)
Conservation of Energy
21(3)
Equilibrium
24(1)
1.6 Principle of Impulse and Linear Momentum
25(1)
Impulse
25(1)
1.7 Principle of Impulse and Angular Momentum
25(4)
Angular Velocity
25(2)
Torque
27(1)
Couple
27(1)
Angular Momentum
28(1)
1.8 System of Particles
29(12)
Impact
33(1)
Direct Central Impact
33(3)
Centre of Mass Coordinates
36(4)
Two Particle Systems
40(1)
1.9 Constraints
41(2)
Degrees of Freedom
42(1)
1.10 Virtual Displacements
43(1)
1.11 Miscellaneous Problems
44(3)
2 Lagrangian Dynamics
47(39)
2.1 Generalized Coordinates
47(4)
Configuration Space
50(1)
Virtual Displacements
50(1)
2.2 Generalized Forces
51(6)
Conservative Forces
54(1)
Non-conservative Forces
55(2)
2.3 D' Alembert's Principle
57(2)
2.4 Lagrange's Equations of Motion
59(5)
2.5 Lagrange's Equations for Conservative Forces
64(5)
Electrical Systems
69(1)
2.6 Lagrange's Equations for Non-conservative Forces
69(3)
Electromagnetic Fields
70(2)
2.7 Systems under Conservative and Non-conservative Forces
72(1)
System of Particles under Frictional Forces
72(3)
2.8 Lagrange's Equations for Nonholonomic Systems
75(3)
Lagrangian Multiplier Method
75(3)
2.9 Generalized Momenta
78(2)
Generalized Momenta for Electromagnetic Fields
80(1)
2.10 Generalized Impulse
80(2)
2.11 The Lagrangian in Special Relativity
82(2)
2.12 Supplementary Problems
84(2)
3 Conservation Laws and Symmetric Properties
86(16)
3.1 Integrals of Motion
86(1)
3.2 Cyclic or Ignorable Coordinates
87(1)
3.3 Homogeneity and Isotropy
88(1)
3.4 Homogeneity in Time and Conservation of Energy
89(1)
3.5 Homogeneity in Space and Conservation of Linear Momentum
90(3)
3.6 Isotropy of Space and Conservation of Angular Momentum
93(2)
3.7 Symmetry and Conservation Laws
95(1)
3.8 The Universal and Fundamental Nature of Conservation Laws
96(1)
3.9 Worked Examples
97(2)
3.10 Supplementary Problems
99(3)
4 Central Force Fields
102(26)
4.1 Central Force Motion
102(5)
4.2 Effective Potential
107(1)
4.3 Inverse Square Law of Forces
108(5)
Paths under Inverse Square Forces
110(1)
Hyperbolic Orbit
111(1)
Elliptic Orbit
112(1)
Parabolic Orbit
112(1)
4.4 Newton's Law of Universal Gravitation
113(4)
4.5 Two Particles Systems
117(3)
Kepler's Law
118(2)
Binary Star Systems
120(1)
4.6 Scattering in Central fields
120(2)
4.7 Worked examples
122(3)
4.7 Supplementary Problems
125(3)
5 Non-lnertial Co-ordinate systems
128(16)
5.1 Moving Coordinate Systems
128(4)
5.2 Motion Relative to Earth
132(2)
5.3 Coriolis Force
134(3)
5.4 Foucault pendulum
137(5)
5.5 Supplementary Problems
142(2)
6 Rigid Body Motion
144(32)
6.1 Fundamentals of Rigid Body Motion
144(1)
6.2 Moment of Inertia
145(3)
Parallel Axis Theorem
146(1)
Perpendicular Axis Theorem
147(1)
6.3 Rigid Body Rotation
148(1)
6.4 Plane Motion of a Rigid Body about a Fixed Axis
149(3)
Compound Pendulum
151(1)
6.5 General Plane Motion of a Rigid Body
152(3)
6.6 General Expression for Moment of Inertia
155(3)
Inertia Ellipsoid 155 Principle Moment of Inertia
156(2)
6.7 The General Motion of a Rigid Body in Space
158(1)
6.8 Pure Rotation of Rigid Bodies
159(6)
6.9 The Euler Angles
165(2)
6.10 Euler's Equations for a Rigid Body
167(4)
6.11 Heavy Symmetrical Top
171(4)
6.12 Supplementary Problems
175(1)
7 Theory of Small Oscillations
176(21)
7.1 Theory
176(3)
7.2 Oscillations with One Degree of Freedom
179(2)
Harmonic Oscillator
178(3)
7.3 Oscillations of Systems with Two and Three Degrees of Freedom
181(4)
Longitudinal Vibrations of Tri-atomic Molecules
181(2)
Two Statistically Coupled Masses
183(2)
7.4 Normal Coordinates and Linear Transformation
185(8)
Coupled Pendulums
186(3)
The Double Pendulum
189(1)
Three Linearly Coupled Masses
190(2)
Coupled Electric Circuits
192(1)
7.5 Worked Example
193(1)
7.6 Supplementary Problems
194(3)
8 Hamilton's Principle
197(11)
8.1 Configuration Space
197(1)
8.2 Hamilton's Principle
198(4)
8.3 Lagrangian Equations and Hamilton's Principle
202(1)
8.4 Applications
203(3)
Harmonic Oscillator
203(1)
Simple Pendulum
204(1)
Motion in a Central Force Field
205(1)
8.5 Supplementary Problems
206(2)
9 Hamlltonian Theory
208(30)
9.1 Phase Space
208(1)
9.2 Hamiltonian Function
208(4)
Hamiltonian for Electromagnetic Fields
209(1)
Hamiltonian in Special Relativity
210(1)
Relativistic Hamiltonian for Electromagnetic Fields
211(1)
9.3 Hamilton's Canonical Equations
212(5)
Harmonic Oscillator
215(2)
Motion in a Central Force Field
217(1)
9.4 Conservation Theorems
217(5)
Homogeneity in Time and Conservation of Energy
220(2)
9.5 Poisson Brackets
222(2)
Fundamental Poisson Brackets
223(1)
9.6 lassical Equations of Motion
224(3)
Integrals of Motion
226(1)
Poisson Theorem
226(1)
9.7 Liouville's Theorem
227(2)
9.8 Infinitesimal Transformations
229(4)
Time Translations
231(1)
Space Translations
232(1)
Rotations
232(1)
9.9 Worked Example
233(2)
9.10 Supplementary Problems
235(3)
10 Canonical Transformations
238(19)
10.1 Canonical Transformations
238(2)
10.2 Generating Functions
240(4)
First Generating function
241(1)
Second Generating function
242(1)
Third Generating function
243(1)
Fourth Generating function
243(1)
10.3 Invariants of Canonical Transformation
244(6)
Hamiltonian
244(1)
Fundamental Poisson Brackets
245(3)
Poisson Brackets
248(1)
Integral Invariants of Poincare
249(1)
10.4 Infinitesimal Transformations
250(2)
10.5 Relativistic Hamilton's principle
252(1)
10.6 Worked Example
253(1)
10.7 Supplementary Problems
254(3)
11 Hamilton - Jacobi Theory
257(15)
11.1 Hamilton-Jacobi Equation
257(2)
11.2 Separation of Variables
259(2)
11.3 Applications
261(7)
One dimensional harmonic oscillator
261(1)
Motion of a Particle under the Action of a Central Field
262(2)
Motion of a Particle in a Uniform Gravitational Field
264(2)
Motion of a Particle in a Field of Fixed Centre of Force
266(2)
11.4 Perturbation Theory
268(2)
11.5 Supplementary Problems
270(2)
Bibliography 272(1)
Answers to Problems 273(4)
Index 277