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:

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