Hamiltonian mechanics with two times: part 1
To start with, we start with Lagrangian mechanics. Lagrangian mechanics states that the variation of the “action” with respect to every dynamical variable is zero. Suppose the action can be written in the form$$S=\int Ld\tau d\sigma$$ Then standard variational methods give the Euler-Lagrange equation$$\frac{\partial L}{\partial x}=\frac{\partial}{\partial\tau}\frac{\partial L}{\partial \frac{\partial x}{\partial \tau}}+\frac{\partial}{\partial\sigma}\frac{\partial L}{\partial \frac{\partial x}{\partial \sigma}}$$ For […]
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