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We revisit the classical problem of 3D shape interpolation and propose a novel, physically plausible approach based on Hamiltonian dynamics. While most prior work focuses on synthetic input shapes, our formulation is designed to be applicable to real-world scans with imperfect input correspondences and various types of noise. To that end, we use recent progress on dynamic thin shell simulation and divergence-free shape deformation and combine them to address the inverse problem of finding a plausible intermediate sequence for two input shapes. In comparison to prior work that mainly focuses on small distortion of consecutive frames, we explicitly model volume preservation and momentum conservation, as well as an anisotropic local distortion model. We argue that, in order to get a robust interpolation for imperfect inputs, we need to model the input noise explicitly which results in an alignment based formulation. Finally, we show a qualitative and quantitative improvement over prior work on a broad range of synthetic and scanned data. Besides being more robust to noisy inputs, our method yields exactly volume preserving intermediate shapes, avoids self-intersections and is scalable to high resolution scans.