The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.
The book introduces classical mechanics. It does so in an informal style with numerous fresh, modern and inter-disciplinary applications assuming no prior knowledge of the necessary mathematics. The book provides a comprehensive and self-contained treatment of the subject matter up to the forefront of research in multiple areas.
Peter Mann completed his undergraduate degree in Chemistry at the University of St Andrews. He is now a PhD student at the University of St Andrews investigating spreading phenomena on complex networks and how antibiotic resistance proliferates on different network topologies.
Inhaltsangabe
Part I: Newtonian Mechanics 1: Introduction 2: Newton's Three Laws 3: Energy and Work 4: Introductory Rotational Dynamics 5: The Harmonic Oscillator 6: Wave Mechanics and Elements of Mathematical Physics Part II: Langrangian Mechanics 7: Introduction 8: Coordinates and Constraints 9: The Stationary Action Principle 10: Constrained Langrangian Mechanics 11: Point Transformations in Langrangian Mechanics 12: The Jacobi Energy Function 13: Symmetries and Langrangian-Hamiltonian-Jacobi Theory 14: Near-Equilibrium Oscillations 15: Virtual Work and d'Alembert's Principle Part III: Canonical Mechanics 16: Introduction 17: The Hamiltonian and Phase Space 18: Hamiltonian's equations and Routhian Reduction 19: Poisson Brackets and Angular momentum 20: Canonical and Gauge Transformations 21: Hamilton-Jacobi Theory 22: Liouville's Theorem and Classical Statistical Mechanics 23: Constrained Hamiltonian Dynamics 24: Autonomous Geometrical Mehcanics 25: The Structure of Phase Space 26: Near-Integrable Systems Part IV: Classical Field Theory 27: Introduction 28: Langrangian Field Theory 29: Hamiltonian Field Theory 30: Clssical Electromagnetism 31: Neother's Theorem for Fields 32: Classical Path-Integrals Part V: Preliminary Mathematics 33: The (Not so?) Basics 34: Matrices 35: Partial Differentiation 36: Legendre Transformations 37: Vector Calculus 38: Differential equations 39: Calculus of Variations Part VI: Advanced Mathematics 40: Linear Algebra 41: Differential Geometry Part VII: Exam Style Questions Appendix A: Noether's Theorem Explored Appendix B: The Action Principle Explored Appendix C: Useful Relations Appendxi D: Poisson and Nambu Brackets Explored Appendix: Canonical Transformations Explored Appendix F: Action-Angle Variables Explored Appendix G: Statistical Mechanics Explored Appendix H: Biographies
Part I: Newtonian Mechanics 1: Introduction 2: Newton's Three Laws 3: Energy and Work 4: Introductory Rotational Dynamics 5: The Harmonic Oscillator 6: Wave Mechanics and Elements of Mathematical Physics Part II: Langrangian Mechanics 7: Introduction 8: Coordinates and Constraints 9: The Stationary Action Principle 10: Constrained Langrangian Mechanics 11: Point Transformations in Langrangian Mechanics 12: The Jacobi Energy Function 13: Symmetries and Langrangian-Hamiltonian-Jacobi Theory 14: Near-Equilibrium Oscillations 15: Virtual Work and d'Alembert's Principle Part III: Canonical Mechanics 16: Introduction 17: The Hamiltonian and Phase Space 18: Hamiltonian's equations and Routhian Reduction 19: Poisson Brackets and Angular momentum 20: Canonical and Gauge Transformations 21: Hamilton-Jacobi Theory 22: Liouville's Theorem and Classical Statistical Mechanics 23: Constrained Hamiltonian Dynamics 24: Autonomous Geometrical Mehcanics 25: The Structure of Phase Space 26: Near-Integrable Systems Part IV: Classical Field Theory 27: Introduction 28: Langrangian Field Theory 29: Hamiltonian Field Theory 30: Clssical Electromagnetism 31: Neother's Theorem for Fields 32: Classical Path-Integrals Part V: Preliminary Mathematics 33: The (Not so?) Basics 34: Matrices 35: Partial Differentiation 36: Legendre Transformations 37: Vector Calculus 38: Differential equations 39: Calculus of Variations Part VI: Advanced Mathematics 40: Linear Algebra 41: Differential Geometry Part VII: Exam Style Questions Appendix A: Noether's Theorem Explored Appendix B: The Action Principle Explored Appendix C: Useful Relations Appendxi D: Poisson and Nambu Brackets Explored Appendix: Canonical Transformations Explored Appendix F: Action-Angle Variables Explored Appendix G: Statistical Mechanics Explored Appendix H: Biographies
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