lecture14: Constraints: integral constraints

Topics covered

• Dido's problem
• Isoperimetric problems
• Isoperimetric problems formulation
• A simplified form of Dido's problem %
• In polar coordinates
• Approach
• Lagrange multiplier refresher
• Lagrange multipliers in functionals
• Euler-Lagrange equations
• Dido's problem
• Dido's problem: constants
• A realistic coast
• The real Carthage (modern Tunis) %
• Dido's problem: constants
• Catenary redux
• Catenary of fixed length
• Equation of Catenary of Fixed Length
• The length of the Catenary
• Catenary of fixed length
• Calculating the functional
• Degenerate solution
• Calculating the functional (energy)
• Energy as a function of length
• Pathologies
• Rigid Extremals
• Interpretation of $\lambda$