lecture08: invariance of the E-L equations, and degenerate equations

Topics covered

%
• Invariance of the E-L equations
• Euler-Lagrange equation
• Invariance of the E-L equations
• Notation
• Transforming $dy/dx$
• Transforming functional
• Fixed end-point problem
• Relation between extremals
• Some of the details %
• Some of the details
• Example
• Degenerate cases
• Example
• Theorem %
• Invariance of the E-L equations %
• Geodesics %
• Geodesic on a surface of revolution %
• Geodesic on cone