Practice question · Match the pairs
Match each object to its definition.
- Functional
- Variation
- Euler–Lagrange equation
- Condition the optimal path obeys at every instant
- Maps an entire curve to one number
- A small deformation of the candidate path
- The path’s rate of change entering
Hints
- Separate the score from the small deformation from the condition.
- One object assigns a single number to an entire curve.
Show the answer
- Functional → Maps an entire curve to one number
- Variation → A small deformation of the candidate path
- Euler–Lagrange equation → Condition the optimal path obeys at every instant
- → The path’s rate of change entering
Why
Score, perturbation, optimality condition, and slope, the four pieces of every variational problem.
Practise Calculus of Variations
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