Classical Mechanics focuses on the use of calculus to solve problems in classical mechanics. Topics covered include motion in one dimension and three dimensions; the harmonic oscillator; vector algebra and vector calculus; and systems of particles. Coordinate systems and central forces are also discussed, along with rigid bodies and Lagrangian mechanics.

Comprised of 13 chapters, this book begins with a crash course (or brief refresher) in the BASIC computer language and its immediate application to solving the harmonic oscillator. The discussion then turns to kinematics and dynamics in one dimension; three-dimensional harmonic oscillators; moving and rotating coordinate systems; and central forces in relation to potential energy and angular momentum. Subsequent chapters deal with systems of particles and rigid bodies as well as statics, Lagrangian mechanics, and fluid mechanics. The last chapter is devoted to the theory of special relativity and addresses concepts such as spacetime coordinates, simultaneity, Lorentz transformations, and the Doppler effect.

This monograph is written to help students learn to use calculus effectively to solve problems in classical mechanics.

Contenu

Preface
1 Conversational Basic
1.1 Getting Started
1.2 Elegant Output
1.3 Sometimes More is Really Less
1.4 Into the Wild Blue
2 One-Dimensional Motion
2.1 Kinematics in One Dimension
2.2 Dynamics in One Dimension
2.3 Constant Force
2.4 Force as a Function of Time
2.5 Force as a Function of Position
2.6 Force as a Function of Velocity
3 The Harmonic Oscillator
3.1 Introduction
3.2 Simple Harmonic Oscillator
3.3 Power Series Representation of an Arbitrary Function
3.4 Damped Harmonic Oscillator
3.5 Forced Harmonic Oscillator
3.6 Application to AC Circuits
3.7 Simple Pendulum
3.8 Physical Pendulum
4 Vectors
4.1 Introduction
4.2 Vector Algebra
4.3 Vector Multiplication
4.4 Coordinate Systems
4.5 Vector Calculus
4.6 Vector Differential Operators
5 Motion in Three Dimensions
5.1 Introduction
5.2 Separable Forces
5.3 Three-Dimensional Harmonic Oscillator
5.4 Potential Energy Function
5.5 Motion in Electromagnetic Fields
6 Coordinate Systems
6.1 Introduction
6.2 Plane Polar Coordinates
6.3 Cylindrical Polar Coordinates
6.4 Spherical Polar Coordinates
6.5 Moving Coordinate Systems
6.6 Rotating Coordinate Systems
6.7 Motion Observed on the Rotating Earth
6.8 Foucault Pendulum
7 Central Forces
7.1 Introduction
7.2 Potential Energy and Central Forces
7.3 Angular Momentum and Central Forces
7.4 Inverse-Square Force
7.5 Kepler's Laws
7.6 Orbital Transfers and "Gravitational Boosts"
7.7 Radial Oscillations about a Circular Orbit
7.8 Gravity
7.9 Rutherford Scattering
8 Systems of Particles
8.1 N Particles, the General Case
8.2 Momentum
8.3 Motion with a Variable Mass-Rockets
8.4 Motion with a Variable Mass-Conveyor Belts
8.5 Collisions
8.6 Center of Mass Frame
9 Rigid Bodies
9.1 Center of Mass
9.2 Angular Momentum
9.3 Rotation about an Axis
9.4 Moment of Inertia Theorems
9.5 The Inertia Tensor
9.6 Principal Axes
9.7 Kinetic Energy
9.8 Euler's Equations
10 Lagrangian Mechanics
10.1 Introduction
10.2 Generalized Coordinates
10.3 Generalized Forces
10.4 Lagrange's Equations
10.5 Elementary Examples
10.6 Systems with Constraints
10.7 Applications
10.8 Ignorable Coordinates
10.9 Lagrangian Mechanics and a Rotating Top
10.10 Hamilton's Equations
10.11 Hamilton's Principle
11 Statics
11.1 Introduction
11.2 Plane Trusses
11.3 Method of Joints
11.4 Method of Sections
11.5 Cables under Distributed Loads
11.6 Parabolic Cables
11.7 Catenary Cables
11.8 Cables with Concentrated Loads
12 Fluid Mechanics
12.1 Introduction
12.2 Hydrostatics: Fluids at Rest
12.3 Moving with the Flow
12.4 Hydrodynamics
13 Special Relativity
13.1 Introduction
13.2 Galilean Relativity
13.3 Historical Background
13.4 Einsteinean Relativity/Spacetime Coordinates
13.5 Simultaneity
13.6 Lorentz Transformations
13.7 Application of the Lorentz Transformations
13.8 Minkowski Diagrams
13.9 Velocity Transformation
13.10 Doppler Effect
13.11 Momentum and Mass-Energy
13.12 Relativistic Mass
Appendices
A Conversational Pascal
B Calculus Review
C Multiple Integrals
D Matrix Multiplication
Index