Modern Classical Mechanics (Instructor Res. n. 1 of 5, Solution Manual, Solutions)

Cover
Half-title
Title page
Copyright information
Dedication
Contents
Preface
Acknowledgements and Credits
Notation and Conventions
Useful Relations
Part I
	1 Newtonian Particle Mechanics
		1.1 Inertial Frames and the Galilean Transformation
		1.2 Newton's Laws of Motion
		1.3 One-Dimensional Motion: Drag Forces
		1.4 Oscillation in One-Dimensional Motion
		1.5 Resonance
		1.6 Motion in Two or Three Dimensions
		1.7 Systems of Particles
		1.8 Conservation Laws
		1.9 Collisions
		1.10 Forces of Nature
		1.11 Summary
		Problems
	2 Relativity
		2.1 Einstein's Postulates and the Lorentz Transformation
		2.2 Relativistic Kinematics
		2.3 Relativistic Dynamics
		2.4 Summary
		Problems
	3 The Variational Principle
		3.1 Fermat's Principle
		3.2 The Calculus of Variations
		3.3 Geodesics
		3.4 Brachistochrone
		3.5 Several Dependent Variables
		3.6 Mechanics from a Variational Principle
		3.7 Motion in a Uniform Gravitational Field
		3.8 Arbitrary Potential Energies
		3.9 Summary
		Problems
	4 Lagrangian Mechanics
		4.1 Nonconservative Forces
		4.2 Forces of Constraint and Generalized Coordinates
		4.3 Hamilton's Principle
		4.4 Generalized Momenta and Cyclic Coordinates
		4.5 Systems of Particles
		4.6 The Hamiltonian
		4.7 When is H [neq] E?
		4.8 The Moral of Constraints
		4.9 Small Oscillations about Equilibrium
		4.10 Recap
		Problems
	5 From Classical to Quantum and Back
		5.1 Classical Waves
		5.2 Two-Slit Experiments and Quantum Mechanics
		5.3 Feynman Sum-over-Paths
		5.4 Helium Atoms and the Two Slits, Revisited
		5.5 The Emergence of the Classical Trajectory
		5.6 Why Hamilton's Principle?
		5.7 The Jacobi Action
		5.8 Summary
		Problems
Part II
	6 Constraints and Symmetries
		6.1 Contact Forces
		6.2 Symmetries and Conservation Laws: A Preview
		6.3 Cyclic Coordinates and Generalized Momenta
		6.4 A Less Straightforward Example
		6.5 Infinitesimal Transformations
		6.6 Symmetry
		6.7 Noether's Theorem
		6.8 Some Comments on Symmetries
		6.9 Summary
		Problems
	7 Gravitation
		7.1 Central Forces
		7.2 The Two-Body Problem
		7.3 The Effective Potential Energy
		7.4 The Shape of Central-Force Orbits
		7.5 Bertrand's Theorem
		7.6 Orbital Dynamics
		7.7 The Virial Theorem in Astrophysics
		7.8 Summary
		Problems
	8 Electromagnetism
		8.1 Gravitation Revisited
		8.2 The Lorentz Force Law
		8.3 The Lagrangian for Electromagnetism
		8.4 The Two-Body Problem, Once Again
		8.5 Coulomb Scattering
		8.6 Motion in a Uniform Magnetic Field
		8.7 Relativistic Effects and the Electromagnetic Force
		8.8 Summary
		Problems
	9 Accelerating Frames
		9.1 Linearly Accelerating Frames
		9.2 Rotating Frames
		9.3 Pseudoforces in Rotating Frames
		9.4 Pseudoforces on Earth
		9.5 Spacecraft Rendezvous and Docking
		9.6 Summary
		Problems
	10 From Black Holes to Random Forces
		10.1 Beyond Newtonian Gravity
		10.2 The Schwarzschild Geometry
		10.3 Geodesics in the Schwarzschild Spacetime
		10.4 The Event Horizon and Black Holes
		10.5 Magnetic Gravity
		10.6 Gauge Symmetry
		10.7 Stochastic Forces
		10.8 Summary
		Problems
Part III
	11 Hamiltonian Formulation
		11.1 Legendre Transformations
		11.2 Hamilton's Equations
		11.3 Phase Space
		11.4 Canonical Transformations
		11.5 Poisson Brackets
		11.6 Poisson Brackets and Noether's Theorem
		11.7 Liouville's Theorem
		11.8 Summary
		Problems
	12 Rigid-Body Dynamics
		12.1 Rotation About a Fixed Axis
		12.2 Euler's Theorem
		12.3 Rotation Matrices and the Body Frame
		12.4 The Euler Angles
		12.5 Infinitesimal Rotations
		12.6 Angular Momentum
		12.7 Principal Axes
		12.8 Torque
		12.9 Kinetic Energy
		12.10 Potential Energy
		12.11 Torque-Free Dynamics Using Euler Angles
		12.12 Euler's Equations of Motion and Stability
		12.13 Gyroscopes
		12.14 Summary
		Problems
	13 Coupled Oscillators
		13.1 Linear Systems of Masses and Springs
		13.2 More Realistic Bound Systems
		13.3 Vibrational Degrees of Freedom
		13.4 The Continuum Limit
		13.5 Summary
		Problems
	14 Complex Systems
		14.1 Integrability
		14.2 Conservative Chaos
		14.3 Dissipative Chaos
		14.4 The Logistic Map
		14.5 Perturbation Techniques
		14.6 Numerical Techniques
		14.7 Summary
		Problems
	15 Seeds of Quantization
		15.1 Hamilton–Jacobi Theory
		15.2 Hamilton's Characteristic Function
		15.3 Action Angle Variables
		15.4 Adiabatic Invariants
		15.5 Early Quantum Theory
		15.6 Optics: From Waves to Rays
		15.7 Schrödinger's Wave Mechanics
		15.8 Quantum Operators and the Bracket
		15.9 A Hint at Quantum Time Evolution
		15.10 Summary
		Problems
Appendices
	A Coordinate Systems
	B Integral Theorems
	C Dimensional Reasoning
	D Fractal Dimension
	E A Brief on Special Polynomials
	F Taylor Series
Further Reading
Index