lecture17: Free end points and natural boundary conditions

Topics covered

• Non-fixed end point problems
• Example: freely supported beam
• Example: beam fixed at one end point
• Perturbation again
• Space of Perturbations
• Same derivation of the first variation
• The first variation
• Euler-Lagrange again
• Extensions (i)
• Extensions (ii)
• Bent beam
• Bent Beam: see earlier
• Bent Beam: Example 1
• Bent Beam Example 2
• Bent Beam Example 3
• Bent beam, end-points conditions
• Bent Beam Example 4
• Optimal control with terminal costs
• Terminal costs reformulation
• Terminal costs: example
• Terminal costs and E-L equations
• Terminal costs and boundary conditions
• Example: stimulated plant growth
• Plant growth problem statement
• Plant growth
• Plant growth: E-L equations
• Plant growth: natural boundary cond.
• Plant growth solution
• Optimal Control
• Freeing up the independent variable %
• Terminal costs: example