lecture05: autonomous problems: the catenary

Topics covered

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• The first variation
• Euler-Lagrange equation
• Autonomous case
• Proof of Theorem 2.3.1
• The Catenary
• The Catenary, reformulation
• The Catenary (iii)
• The Catenary (iv)
• The Catenary (v) %
• The Catenary (v)
• The Catenary (vi)
• Catenaries of different $L$
• Finding the constants
• Existence of a solution
• Calculating the functional
• The length of the Catenary %
• Existence of a solution
• Catenary addendum
• The shape of an arch
• Other arches
• Some history