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Classical Mechanics
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Overview
Classical mechanics is the study of the motion of particles and rigid bodies under the influence of given forces. It applies to the enormous range of motions between the atomic scale, where quantum effects dominate, and the cosmological scale, where general relativity provides the framework. Coupled with classical electromagnetic theory it provides the basis for sophisticated technologies such as plasma physics, accelerator design, space technology, and more.
In this edition, the authors have included the fundamental subjects of Lagrangian mechanics, Hamiltonian mechanics, rigidbody motion, actionangle variables, perturbation theory, and motion with speeds approaching that of light, showing how these theories can be applied to a variety of problems. They treat central motion, the motion of planets and satellites, in detail. They also develop the theory of small vibrations governing resonant systems of all kinds, analyze the motion of particles in high energy accelerators and describe the motion of spinning systems, important for space technology. Nonstandard topics like the NavierStokes equation and the inverted pendulum are included.
A number of exercises are provided and most chapters contain references to relevant books and other literature.
Product Details
ISBN13:  9780486680637 

Publisher:  Dover Publications 
Publication date:  08/18/1994 
Series:  Dover Books on Physics Series 
Edition description:  Unabridged 
Pages:  416 
Sales rank:  1,267,171 
Product dimensions:  5.42(w) x 8.54(h) x 0.81(d) 
Read an Excerpt
Classical mechanics is the study of the motion of particles and rigid bodies under the influence of given forces. It applies to the enormous range of motions between the atomic scale, where quantum effects dominate, and the cosmological scale, where general relativity provides the framework. Coupled with classical electromagnetic theory it provides the basis for sophisticated technologies such as plasma physics, accelerator design, space technology, and more.
In this edition, the authors have included the fundamental subjects of Lagrangian mechanics, Hamiltonian mechanics, rigidbody motion, actionangle variables, perturbation theory, and motion with speeds approaching that of light, showing how these theories can be applied to a variety of problems. They treat central motion, the motion of planets and satellites, in detail. They also develop the theory of small vibrations governing resonant systems of all kinds, analyze the motion of particles in high energy accelerators and describe the motion of spinning systems, important for space technology. Nonstandard topics like the NavierStokes equation and the inverted pendulum are included.
A number of exercises are provided and most chapters contain references to relevant books and other literature.
First Chapter
Classical mechanics is the study of the motion of particles and rigid bodies under the influence of given forces. It applies to the enormous range of motions between the atomic scale, where quantum effects dominate, and the cosmological scale, where general relativity provides the framework. Coupled with classical electromagnetic theory it provides the basis for sophisticated technologies such as plasma physics, accelerator design, space technology, and more.
In this edition, the authors have included the fundamental subjects of Lagrangian mechanics, Hamiltonian mechanics, rigidbody motion, actionangle variables, perturbation theory, and motion with speeds approaching that of light, showing how these theories can be applied to a variety of problems. They treat central motion, the motion of planets and satellites, in detail. They also develop the theory of small vibrations governing resonant systems of all kinds, analyze the motion of particles in high energy accelerators and describe the motion of spinning systems, important for space technology. Nonstandard topics like the NavierStokes equation and the inverted pendulum are included.
A number of exercises are provided and most chapters contain references to relevant books and other literature.
Table of Contents
Chapter 1. Kinematics of Particles
1. Introduction
2. Definition and Description of Particles
3. Velocity
4. Acceleration
5. Special Coordinate Systems
6. Vector Algebra
7. Kinematics and Measurement
Exercises
Chapter 2. The Laws of Motion
8. Mass
9. Momentum and Force
10. Kinetic Energy
11. Potential Energy
12. Conservation of Energy
13. Angular Momentum
14. Rigid Body Rotating about a Fixed Point
15. A Theorem on Quadratic Functions
16. Inertial and Gravitational Masses
Exercises
Chapter 3. Conservative Systems with One Degree of Freedom
17. The Oscillator
18. The Plan Pendulum
19. ChildLangmuir Law
Exercises
Chapter 4. TwoParticle Systems
20. Introduction
21. Reduced Mass
22. Relative Kinetic Energy
23. Laboratory and CenterofMass Systems
24. Central Motion
Exercises
Chapter 5. TimeDependent Forces and Nonconservative Motion
25. Introduction
26. The Inverted Pedulum
27. Rocket Motion
28. Atmospheric Drag
29. The PoyntingRobertson Effect
30. The Damped Oscillator
Exercises
Chapter 6. Lagrange's Equations of Motion
31. Derivation of Lagrange's Equations
32. The Lagrangian Function
33. The Jacobian Integral
34. Momentum Integrals
35. Charged Particle in an Electromagnetic Field
Exercises
Chapter 7. Applications of Lagrange's Equations
36. Orbits under a Central Force
37. Kepler Motion
38. Rutherford Scattering
39. The Spherical Pendulum
40. Larmor's Theorem
41. The Cylindrical Magnetron
Exercises
Chapter 8. Small Oscillations
42. Oscillations of a Natural System
43. Systems with Few Degrees of Freedom
44. "The Stretched String, Discrete Masses"
45. Reduction of the Number of Degrees of Freedom
46. Laplace Transforms and Dissipative Systems
Exercises
Chapter 9. Rigid Bodies
47. Displacements of a Rigid Body
48. Euler's Angles
49. Kinematics of Rotation
50. The Momental Ellipsoid
51. The Free Rotator
52. Euler's Equations of Motion
Exercises
Chapter 10. Hamiltonian Theory
53. Hamilton's Equations
54. Hamilton's Equations in Various Coordinate Systems
55. Charged Particle in an Electromagnetic Field
56. The Virial Theorem
57. Variational Principles
58. Contact Transformations
59. Alternative Forms of Contact Transformations
60. Alternative Forms of the Equations of Motion
Exercises
Chapter 11. The HamiltonJacobi Method
61. The HamiltonJacobi Equation
62. Action and Angle VariablesPeriodic Systems
63. Separable MulitplyPeriodic Systems
64. Applications
Exercises
Chapter 12. Infinitesimal Contact Transformations
65. Transformation Theory of Classical Dynamics
66. Poisson Brackets
67. Jacobi's Identity
68. Poisson Brackets in Quantum Mechanics
Exercises
Chapter 13. Further Development of Transformation Theory
69. Notation
70. Integral Invariants and Liouville's Theorem
71. Lagrange Brackets
72. Change of Independent Variable
73. Extended Contact Transformations
74. Perturbation Theroy
75. Stationary State Perturbation Theory
76. TimeDependent Perturbation Theory
77. Quasi Coordinates and Quasi Momenta
Exercises
Chapter 14. Special Applications
78. Noncentral Forces
79. Spin Motion
80. Variational Principles in Rocket Motion
81. The Boltzmann and NavierStokes Equations
Chapter 15. Continuous Media and Fields
82. The Stretched String
83. EnergyMomentum Relations
84. ThreeDimensional Media and Fields
85. Hamiltonian Form of Field Theory
Exercises
Chapter 16. Introduction to Special Relativity Theory
86. Introduction
87. SpaceTime and Lorentz Transformation
88. The Motion of a Free Particle
89. Charged Particle in an Electromagnetic Field
90. Hamiltonian Formulation of the Equations of Motion
91. Transformation Theory and the Lorentz Group
92. Thomas Precession
Exercises
Chapter 17. The Orbits of Particles in High Energy Accelerators
93. Introduction
94. Equilibrium Orbits
95. Betatron Oscillations
96. Weak Focusing Accelerators
97. Strong Focusing Accelerators
98. Acceleration and Synchrotron Oscillations
Appendix I Riemannian Geometry
Appendix II Linear Vector Spaces
Appendix III Group Theory and Molecular Vibrations
Apendix IV Quaternions and Pauli Spin Matrices
Index
Reading Group Guide
Chapter 1. Kinematics of Particles
1. Introduction
2. Definition and Description of Particles
3. Velocity
4. Acceleration
5. Special Coordinate Systems
6. Vector Algebra
7. Kinematics and Measurement
Exercises
Chapter 2. The Laws of Motion
8. Mass
9. Momentum and Force
10. Kinetic Energy
11. Potential Energy
12. Conservation of Energy
13. Angular Momentum
14. Rigid Body Rotating about a Fixed Point
15. A Theorem on Quadratic Functions
16. Inertial and Gravitational Masses
Exercises
Chapter 3. Conservative Systems with One Degree of Freedom
17. The Oscillator
18. The Plan Pendulum
19. ChildLangmuir Law
Exercises
Chapter 4. TwoParticle Systems
20. Introduction
21. Reduced Mass
22. Relative Kinetic Energy
23. Laboratory and CenterofMass Systems
24. Central Motion
Exercises
Chapter 5. TimeDependent Forces and Nonconservative Motion
25. Introduction
26. The Inverted Pedulum
27. Rocket Motion
28. Atmospheric Drag
29. The PoyntingRobertson Effect
30. The Damped Oscillator
Exercises
Chapter 6. Lagrange's Equations of Motion
31. Derivation of Lagrange's Equations
32. The Lagrangian Function
33. The Jacobian Integral
34. Momentum Integrals
35. Charged Particle in an Electromagnetic Field
Exercises
Chapter 7. Applications of Lagrange's Equations
36. Orbits under a Central Force
37. Kepler Motion
38. Rutherford Scattering
39. The Spherical Pendulum
40. Larmor's Theorem
41. The Cylindrical Magnetron
Exercises
Chapter 8. Small Oscillations
42. Oscillations of a Natural System
43. Systems with Few Degrees of Freedom
44. "The Stretched String, Discrete Masses"
45. Reduction of the Number of Degrees of Freedom
46. Laplace Transforms and Dissipative Systems
Exercises
Chapter 9. Rigid Bodies
47. Displacements of a Rigid Body
48. Euler's Angles
49. Kinematics of Rotation
50. The Momental Ellipsoid
51. The Free Rotator
52. Euler's Equations of Motion
Exercises
Chapter 10. Hamiltonian Theory
53. Hamilton's Equations
54. Hamilton's Equations in Various Coordinate Systems
55. Charged Particle in an Electromagnetic Field
56. The Virial Theorem
57. Variational Principles
58. Contact Transformations
59. Alternative Forms of Contact Transformations
60. Alternative Forms of the Equations of Motion
Exercises
Chapter 11. The HamiltonJacobi Method
61. The HamiltonJacobi Equation
62. Action and Angle VariablesPeriodic Systems
63. Separable MulitplyPeriodic Systems
64. Applications
Exercises
Chapter 12. Infinitesimal Contact Transformations
65. Transformation Theory of Classical Dynamics
66. Poisson Brackets
67. Jacobi's Identity
68. Poisson Brackets in Quantum Mechanics
Exercises
Chapter 13. Further Development of Transformation Theory
69. Notation
70. Integral Invariants and Liouville's Theorem
71. Lagrange Brackets
72. Change of Independent Variable
73. Extended Contact Transformations
74. Perturbation Theroy
75. Stationary State Perturbation Theory
76. TimeDependent Perturbation Theory
77. Quasi Coordinates and Quasi Momenta
Exercises
Chapter 14. Special Applications
78. Noncentral Forces
79. Spin Motion
80. Variational Principles in Rocket Motion
81. The Boltzmann and NavierStokes Equations
Chapter 15. Continuous Media and Fields
82. The Stretched String
83. EnergyMomentum Relations
84. ThreeDimensional Media and Fields
85. Hamiltonian Form of Field Theory
Exercises
Chapter 16. Introduction to Special Relativity Theory
86. Introduction
87. SpaceTime and Lorentz Transformation
88. The Motion of a Free Particle
89. Charged Particle in an Electromagnetic Field
90. Hamiltonian Formulation of the Equations of Motion
91. Transformation Theory and the Lorentz Group
92. Thomas Precession
Exercises
Chapter 17. The Orbits of Particles in High Energy Accelerators
93. Introduction
94. Equilibrium Orbits
95. Betatron Oscillations
96. Weak Focusing Accelerators
97. Strong Focusing Accelerators
98. Acceleration and Synchrotron Oscillations
Appendix I Riemannian Geometry
Appendix II Linear Vector Spaces
Appendix III Group Theory and Molecular Vibrations
Apendix IV Quaternions and Pauli Spin Matrices
Index
Interviews
Chapter 1. Kinematics of Particles
1. Introduction
2. Definition and Description of Particles
3. Velocity
4. Acceleration
5. Special Coordinate Systems
6. Vector Algebra
7. Kinematics and Measurement
Exercises
Chapter 2. The Laws of Motion
8. Mass
9. Momentum and Force
10. Kinetic Energy
11. Potential Energy
12. Conservation of Energy
13. Angular Momentum
14. Rigid Body Rotating about a Fixed Point
15. A Theorem on Quadratic Functions
16. Inertial and Gravitational Masses
Exercises
Chapter 3. Conservative Systems with One Degree of Freedom
17. The Oscillator
18. The Plan Pendulum
19. ChildLangmuir Law
Exercises
Chapter 4. TwoParticle Systems
20. Introduction
21. Reduced Mass
22. Relative Kinetic Energy
23. Laboratory and CenterofMass Systems
24. Central Motion
Exercises
Chapter 5. TimeDependent Forces and Nonconservative Motion
25. Introduction
26. The Inverted Pedulum
27. Rocket Motion
28. Atmospheric Drag
29. The PoyntingRobertson Effect
30. The Damped Oscillator
Exercises
Chapter 6. Lagrange's Equations of Motion
31. Derivation of Lagrange's Equations
32. The Lagrangian Function
33. The Jacobian Integral
34. Momentum Integrals
35. Charged Particle in an Electromagnetic Field
Exercises
Chapter 7. Applications of Lagrange's Equations
36. Orbits under a Central Force
37. Kepler Motion
38. Rutherford Scattering
39. The Spherical Pendulum
40. Larmor's Theorem
41. The Cylindrical Magnetron
Exercises
Chapter 8. Small Oscillations
42. Oscillations of a Natural System
43. Systems with Few Degrees of Freedom
44. "The Stretched String, Discrete Masses"
45. Reduction of the Number of Degrees of Freedom
46. Laplace Transforms and Dissipative Systems
Exercises
Chapter 9. Rigid Bodies
47. Displacements of a Rigid Body
48. Euler's Angles
49. Kinematics of Rotation
50. The Momental Ellipsoid
51. The Free Rotator
52. Euler's Equations of Motion
Exercises
Chapter 10. Hamiltonian Theory
53. Hamilton's Equations
54. Hamilton's Equations in Various Coordinate Systems
55. Charged Particle in an Electromagnetic Field
56. The Virial Theorem
57. Variational Principles
58. Contact Transformations
59. Alternative Forms of Contact Transformations
60. Alternative Forms of the Equations of Motion
Exercises
Chapter 11. The HamiltonJacobi Method
61. The HamiltonJacobi Equation
62. Action and Angle VariablesPeriodic Systems
63. Separable MulitplyPeriodic Systems
64. Applications
Exercises
Chapter 12. Infinitesimal Contact Transformations
65. Transformation Theory of Classical Dynamics
66. Poisson Brackets
67. Jacobi's Identity
68. Poisson Brackets in Quantum Mechanics
Exercises
Chapter 13. Further Development of Transformation Theory
69. Notation
70. Integral Invariants and Liouville's Theorem
71. Lagrange Brackets
72. Change of Independent Variable
73. Extended Contact Transformations
74. Perturbation Theroy
75. Stationary State Perturbation Theory
76. TimeDependent Perturbation Theory
77. Quasi Coordinates and Quasi Momenta
Exercises
Chapter 14. Special Applications
78. Noncentral Forces
79. Spin Motion
80. Variational Principles in Rocket Motion
81. The Boltzmann and NavierStokes Equations
Chapter 15. Continuous Media and Fields
82. The Stretched String
83. EnergyMomentum Relations
84. ThreeDimensional Media and Fields
85. Hamiltonian Form of Field Theory
Exercises
Chapter 16. Introduction to Special Relativity Theory
86. Introduction
87. SpaceTime and Lorentz Transformation
88. The Motion of a Free Particle
89. Charged Particle in an Electromagnetic Field
90. Hamiltonian Formulation of the Equations of Motion
91. Transformation Theory and the Lorentz Group
92. Thomas Precession
Exercises
Chapter 17. The Orbits of Particles in High Energy Accelerators
93. Introduction
94. Equilibrium Orbits
95. Betatron Oscillations
96. Weak Focusing Accelerators
97. Strong Focusing Accelerators
98. Acceleration and Synchrotron Oscillations
Appendix I Riemannian Geometry
Appendix II Linear Vector Spaces
Appendix III Group Theory and Molecular Vibrations
Apendix IV Quaternions and Pauli Spin Matrices
Index
Recipe
Chapter 1. Kinematics of Particles
1. Introduction
2. Definition and Description of Particles
3. Velocity
4. Acceleration
5. Special Coordinate Systems
6. Vector Algebra
7. Kinematics and Measurement
Exercises
Chapter 2. The Laws of Motion
8. Mass
9. Momentum and Force
10. Kinetic Energy
11. Potential Energy
12. Conservation of Energy
13. Angular Momentum
14. Rigid Body Rotating about a Fixed Point
15. A Theorem on Quadratic Functions
16. Inertial and Gravitational Masses
Exercises
Chapter 3. Conservative Systems with One Degree of Freedom
17. The Oscillator
18. The Plan Pendulum
19. ChildLangmuir Law
Exercises
Chapter 4. TwoParticle Systems
20. Introduction
21. Reduced Mass
22. Relative Kinetic Energy
23. Laboratory and CenterofMass Systems
24. Central Motion
Exercises
Chapter 5. TimeDependent Forces and Nonconservative Motion
25. Introduction
26. The Inverted Pedulum
27. Rocket Motion
28. Atmospheric Drag
29. The PoyntingRobertson Effect
30. The Damped Oscillator
Exercises
Chapter 6. Lagrange's Equations of Motion
31. Derivation of Lagrange's Equations
32. The Lagrangian Function
33. The Jacobian Integral
34. Momentum Integrals
35. Charged Particle in an Electromagnetic Field
Exercises
Chapter 7. Applications of Lagrange's Equations
36. Orbits under a Central Force
37. Kepler Motion
38. Rutherford Scattering
39. The Spherical Pendulum
40. Larmor's Theorem
41. The Cylindrical Magnetron
Exercises
Chapter 8. Small Oscillations
42. Oscillations of a Natural System
43. Systems with Few Degrees of Freedom
44. "The Stretched String, Discrete Masses"
45. Reduction of the Number of Degrees of Freedom
46. Laplace Transforms and Dissipative Systems
Exercises
Chapter 9. Rigid Bodies
47. Displacements of a Rigid Body
48. Euler's Angles
49. Kinematics of Rotation
50. The Momental Ellipsoid
51. The Free Rotator
52. Euler's Equations of Motion
Exercises
Chapter 10. Hamiltonian Theory
53. Hamilton's Equations
54. Hamilton's Equations in Various Coordinate Systems
55. Charged Particle in an Electromagnetic Field
56. The Virial Theorem
57. Variational Principles
58. Contact Transformations
59. Alternative Forms of Contact Transformations
60. Alternative Forms of the Equations of Motion
Exercises
Chapter 11. The HamiltonJacobi Method
61. The HamiltonJacobi Equation
62. Action and Angle VariablesPeriodic Systems
63. Separable MulitplyPeriodic Systems
64. Applications
Exercises
Chapter 12. Infinitesimal Contact Transformations
65. Transformation Theory of Classical Dynamics
66. Poisson Brackets
67. Jacobi's Identity
68. Poisson Brackets in Quantum Mechanics
Exercises
Chapter 13. Further Development of Transformation Theory
69. Notation
70. Integral Invariants and Liouville's Theorem
71. Lagrange Brackets
72. Change of Independent Variable
73. Extended Contact Transformations
74. Perturbation Theroy
75. Stationary State Perturbation Theory
76. TimeDependent Perturbation Theory
77. Quasi Coordinates and Quasi Momenta
Exercises
Chapter 14. Special Applications
78. Noncentral Forces
79. Spin Motion
80. Variational Principles in Rocket Motion
81. The Boltzmann and NavierStokes Equations
Chapter 15. Continuous Media and Fields
82. The Stretched String
83. EnergyMomentum Relations
84. ThreeDimensional Media and Fields
85. Hamiltonian Form of Field Theory
Exercises
Chapter 16. Introduction to Special Relativity Theory
86. Introduction
87. SpaceTime and Lorentz Transformation
88. The Motion of a Free Particle
89. Charged Particle in an Electromagnetic Field
90. Hamiltonian Formulation of the Equations of Motion
91. Transformation Theory and the Lorentz Group
92. Thomas Precession
Exercises
Chapter 17. The Orbits of Particles in High Energy Accelerators
93. Introduction
94. Equilibrium Orbits
95. Betatron Oscillations
96. Weak Focusing Accelerators
97. Strong Focusing Accelerators
98. Acceleration and Synchrotron Oscillations
Appendix I Riemannian Geometry
Appendix II Linear Vector Spaces
Appendix III Group Theory and Molecular Vibrations
Apendix IV Quaternions and Pauli Spin Matrices
Index