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This is a reformulation of Newton's Laws of Motion, developed by W. R. Hamilton and J. L. Lagrange, using Hamilton's principle of least action and then further analysing the resultant formulae using methods in calculus of variations.

Calculus of Variations

• Brachistochrone Construction Here one can see a graph of the brachistochrone for the given endpoint. Java applet.
• Equations of motion The site is dedicated to equations of motion: discussion, summary, problems.
• Lagrangian and Hamiltonian Mechanics A detailed introduction to the basic features and mathematical formalisms involved.
• Lagrangians and Hamiltonians for High School Students A discussion of Lagrangian and Hamiltonian dynamics is presented at a level which should be suitable for advanced high school students.
• Phase-space This site is about phase-space metric including Non-Hamiltonian system, time evolution, poisson brackets.
• The Brachistichrone Problem A Java applet which illustrates the solution to the Brachistichrone problem.
• The Principle of Least Action An overview of the historical development of the principle of least action.
• The Principle of Least Action A brief review of the mathematics and physics involved in the principle of least action.

 

 

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