Cats can land on their feet when they are held upside down and released from rest. Divers can perform multiple twists before hitting the water. In both cases, a deformable body with zero total angular momentum rotates itself by executing a sequence of deformations. Following Shapere and Wilczek [1], I will show that the kinematics of reorientation is naturally understood in terms of non-Abelian Berry phase in the space of shapes. As an application of their theory, I analyze the falling cat problem following Montgomery's treatment [2].

I will demonstrate that the shape space of Kane-Scher cat (a simplistic model of cat kinematics) is homeomorphic to the real projective plane and its self-rotation sequence maps to a non-contractible loop that picks up a pi flux.

References:

- Alfred Shapere and Frank Wilczek, “Gauge Kinematics of Deformable Bodies”, in Geometric Phases in Physics, World Scientific, 1989.
- Richard Montgomery, “Gauge Theory of the Falling Cat”, Fields Institute Communications 1, 193 (1993).