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Lecture Notes on Classical Mechanics (A Work in Progress)

Daniel Arovas Department of Physics University of California, San Diego May 8, 2013

Contents
0.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 1 1 1 2 3 3 4 5 6 6 7 8 9 10 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 14 15

0 Reference Materials 0.1 0.2 0.3 Lagrangian Mechanics (mostly) . . . . . . . . . . . . . . . . . . . . . . . . . Hamiltonian Mechanics (mostly) . . . . . . . . . . . . . . . . . . . . . . . . Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Introduction to Dynamics 1.1 Introduction and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 1.1.2 1.2 Newton’s laws of motion . . . . . . . . . . . . . . . . . . . . . . . . Aside : inertial vs. gravitational mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Examples of Motion in One Dimension 1.2.1 1.2.2 1.2.3 1.2.4

Uniform force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uniform force with linear frictional damping . . . . . . . . . . . . . Uniform force with quadratic frictional damping . . . . . . . . . . . Crossed electric and magnetic fields . . . . . . . . . . . . . . . . . .

1.3

Pause for Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Systems of Particles 2.1 2.2 Work-Energy Theorem

Conservative and Nonconservative Forces . . . . . . . . . . . . . . . . . . . 2.2.1 Example : integrating F = −∇U . . . . . . . . . . . . . . . . . . .

2.3

Conservative Forces in Many Particle Systems . . . . . . . . . . . . . . . . i

ii

CONTENTS

2.4 2.5

Linear and Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . Scaling of Solutions for Homogeneous Potentials . . . . . . . . . . . . . . . 2.5.1 2.5.2 Euler’s theorem for homogeneous functions . . . . . . . . . . . . . . Scaled equations of motion . . . . . ....

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