This advanced undergraduate Analytical Mechanics (PDF) textbook begins with the Lagrangian formulation of Analytical Mechanics and then passes directly to the Hamiltonian formulation and the canonical equations; with constraints incorporated through Lagrange multipliers. Hamilton’s Principle and the canonical equations remain the basis of the remainder of the text.
Topics considered for applications include small oscillations; motion in electric and magnetic fields; and rigid body dynamics. The Hamilton-Jacobi approach is developed with special attention to the canonical transformation in order to provide a smooth and logical transition into the study of complex and chaotic systems. Finally; the textbook has a careful treatment of relativistic mechanics and the requirement of Lorentz invariance.
The ebook is enriched with an outline of the history of mechanics; which particularly outlines the importance of the work of Euler; Lagrange; Hamilton and Jacobi.
Numerous exercises with solutions support the exceptionally clear and concise treatment of Analytical Mechanics.