Fig. 3.

Pellicle kinematics: theory. (A) Surface strain (the 2 × 2 matrix C) is derived assuming simple shear along the strips, γ, acting on a reference pellicle. The reference pellicle conformation (i,iii) is defined by a shape and a pellicle conformation, given by the tangent vector fields s₀ and m₀, along the strips and perpendicular to them, or by the angle α₀ between the pelliscle strips and the surface parallels. (ii) Ultrastructure of the pellicle (transmission electron micrograph from ref. 7, Copyright 2001 The Society for the Study of Evolution), and depiction of the sliding between adjacent strips causing the pellicle shear γ. (B) Surface strain, C, is now derived by comparing a reference configuration, (iii), given by r₀(λ) and z₀(λ), where λ is the body coordinate, and a deformed configuration (iv), given by r(λ), z(λ) and the azimuthal displacement relative to a fixed direction ψ(λ). The red point denotes a material particle attached to the pellicle, and ()^′ denotes differentiation with respect to λ. Matching the microstructural (A) and the shape-derived (B) expressions for the strain, we find equations relating pellicle shear, pellicle orientation, shape changes, and azimuthal motions.