lecture18: free and movable end points

Topics covered

• Free end points
• Example: Cantilever
• Free end points
• Example: shortest path
• Example: Orbit Transfer Problem %
• Example: rockets path
• Approach
• Extension of $y$
• Distance
• New distance
• Forming the first variation
• End-point compatibility
• The First Variation
• Deriving Euler-Lagrange equations
• Notation
• The Euler-Lagrange equations
• Including constraints
• Separable constraints
• Simple example: fixed $x$
• Simple example: fixed $y$
• Extension to several dep. var.s
• Simple Example
• Simple example %
• Example %
• Example: a thrown ball