1. A Hamiltonian Formulation of Membrane Dynamics under Axial Symmetry

2. Biological Membranes
Biological membranes are important in many cellular processes such as endocytosis and protein diffusion. We seek to model the dynamic properties of membranes. We use a surface model since membrane thickness is small compared to lateral length scales.

3. Geometric Model

4. Membrane Parameterization

5. Surface Constraint

6. Membrane Free Energy

7. Variational Problem

8. Hamilton-Jacobi Formalism

9. Euler-lagrange Equations

10. Lagrangian Dynamic Formulation

11. Membrane Shape Equation Under Dynamic Equilibrium