Goldstein Classical Mechanics Solutions
Solutions and resources for problems from "Classical Mechanics" by Herbert Goldstein, Charles Poole, and John Safko
About This Resource
Goldstein's "Classical Mechanics" is the gold standard graduate-level mechanics textbook. These resources provide detailed solutions and explanations to help you master Lagrangian and Hamiltonian mechanics.
Graduate Level
PhD-qualifying exam preparation
Complete Coverage
Chapters 1-13 problems
Detailed Steps
Every mathematical step shown
Chapter 1: Survey of Elementary Principles
Newton's laws, constraints, D'Alembert's principle, and generalized coordinates.
Key Topics
- • Mechanics of a particle and system of particles
- • Constraints: holonomic vs. nonholonomic
- • D'Alembert's principle and virtual work
- • Generalized coordinates and velocities
Sample Problems
- 1.1: Conservation of momentum derivation
- 1.8: Rolling constraint problems
- 1.14: Generalized forces calculation
- 1.21: Virial theorem derivation
Chapter 2: Variational Principles and Lagrange's Equations
The calculus of variations, Hamilton's principle, and the Euler-Lagrange equations - the heart of analytical mechanics.
Key Equations
Euler-Lagrange Equation:
$\frac{d}{dt}\frac{\partial L}{\partial \dot{q}_j} - \frac{\partial L}{\partial q_j} = 0$
Lagrangian:
$L = T - V$
Sample Problems
- 2.3: Brachistochrone problem
- 2.7: Geodesics on a sphere
- 2.14: Double pendulum
- 2.18: Lagrangian for EM field
Chapter 8: The Hamilton Equations of Motion
Legendre transformation, canonical momenta, Hamilton's equations, and phase space dynamics.
Key Equations
Hamilton's Equations:
$\dot{q}_i = \frac{\partial H}{\partial p_i}, \quad \dot{p}_i = -\frac{\partial H}{\partial q_i}$
Hamiltonian:
$H = \sum_i p_i \dot{q}_i - L$
Sample Problems
- 8.1: Hamiltonian for central force
- 8.4: Poisson brackets computation
- 8.12: Kepler problem in phase space
- 8.20: Liouville theorem proof
Solution Resources
Homer Reid's Solutions
Comprehensive solutions to the 2nd edition by Homer Reid, covering chapters 1-10 with detailed mathematical derivations.
View Solutions3rd Edition Solutions (Ch. 1-3)
Handwritten comprehensive solutions to problems from chapters 1, 2, and 3 of the 3rd edition.
View PDFQuizlet Step-by-Step
Expert-verified solutions with step-by-step explanations for all chapters.
View on QuizletPhysics is Beautiful Collection
Curated collection of solutions and supplementary materials for Goldstein's textbook.
Browse ResourcesVideo Lectures
While dedicated Goldstein problem-solving videos are rare, these lecture series cover the same material at an advanced level.
Susskind's Theoretical Minimum
Leonard Susskind's famous lecture series covering classical mechanics from a modern theoretical perspective.
View LecturesMIT OpenCourseWare
MIT's 8.223 Classical Mechanics II - covers Lagrangian and Hamiltonian mechanics with problem sessions.
MIT OCWStudy Tips for Goldstein
Essential Prerequisites
- • Multivariable calculus (partial derivatives)
- • Linear algebra (eigenvalues, matrices)
- • Ordinary differential equations
- • Undergraduate mechanics (Newtonian)
Problem-Solving Strategy
- • Identify generalized coordinates first
- • Write kinetic energy in terms of $\dot{q}_i$
- • Identify cyclic coordinates for conservation laws
- • Check dimensions at every step