lecture07: geodesics

Topics covered

• Euler-Lagrange equation
• No explicit $y$ dependence
• Solving
• Geodesics on the unit sphere
• Spherical co-ordinates
• Transformation to spherical co-ord.
• Geodesics on the unit sphere
• The constant
• Geodesics on the unit sphere
• Solving the DE
• Solving the DE (part ii)
• The solution
• Example
• Co-ordinate transformation
• Jacobians
• The Jacobian determinant
• Transforms and integrals
• Geodesics