Generalized elastica in SO(3)

An elastica arm scale.

The concept of a 'deformable arm scale' (completely different from a traditional rigid arm balance) is theoretically introduced and experimentally validated. The idea is not intuitive, but is the result of nonlinear equilibrium kinematics of rods inducing configurational forces, so that deflection of the arms becomes necessary for equilibrium, which would be impossible for a rigid system. In pa...

Deformation by Discrete Elastica

Modeling a physically plausible deformation of a flexible object from its naturally planar (curved) state is a fundamental and challenging topic in digital surface processing with applications to computer animation and game design. We propose a new variational model for detail preserving surface-based deformation of a body based on total curvature energy. We demonstrate the efficacy of the mode...

Elastica with Hinges

Area-constrained planar elastica.

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties; not only can the Euler-Lagrange equation be integrated to provide a quadrature for ...

A coarea-type formula for the relaxation of a generalized elastica functional

We consider the generalized elastica functional defined on L1(R2) as F(u) =  ∫ R2 |∇u|(α +β |div ∇u |∇u| |p)dx, if u ∈ C2(R2), +∞ else, where p > 1, α > 0, β ≥ 0. We study the L1-lower semicontinuous envelope F of F and we prove that, for any u ∈ BV(R2), F(u) can be represented by a coarea-type formula involving suitable collections of W2,p curves that cover the essential boundaries of the le...