feat: optimal control / Hamiltonian mechanics layer

[rororowyourboat]

Problem

GDS has no concept of Hamiltonians, costate equations, adjoint dynamics, or Pontryagin's Maximum Principle. Optimal control derivation is a core technique for dynamical systems that we cannot express.

Proposed Solution

A new package or module for optimal control problems:

• State dynamics + cost functional specification
• Hamiltonian construction (potentially symbolic via SymPy)
• Costate (adjoint) equation derivation
• Pontryagin maximum principle application
• Transversality conditions
• Bang-bang and singular control detection

Could compile to GDS spec: states → Entity, dynamics → Mechanism, controls → Policy.

Motivation

The Homicidal Chauffeur notebook derives optimal pursuit-evasion controls from the Hamiltonian via Pontryagin's principle, including bang-bang switching, costate conservation proofs, and transversality conditions.

Dependencies

• feat(gds-sim): continuous-time ODE integration support #122 (continuous-time ODE integration)
• Optional: SymPy for symbolic derivation

Scope

This is a long-term initiative. Could start with numerical optimal control (direct methods) and add symbolic derivation later.