Geometry within a linear spherical complex

The complex geometry of the spherical pendulum

In this paper we describe the geometry of the energy momentum mapping of the complexified spherical pendulum. For background on the classical spherical pendulum we refer the reader to [4, chpt. IV]. We show that this complex Hamiltonian system is Mumford-Jacobi completely integrable [9, p.3.51–3.53] and admits an analogue of the period lattice [5] and action angle coordinates [4, Apend. D]. Fol...

Complex fuzzy linear systems

A Computer Modeling of Mie-Scattering by Spherical Droplets Within the Atmosphere

The Earth’s atmosphere is an environment replete with particles of differ-ent sizes with various refractive indices which affect the light radiation traveling through it. The Mie scattering theory is one of the well-known light scattering techniques ap-plicable to modeling of electromagnetic scattering from tiny atmospheric particles or aerosols floating in the air or within the clouds. In this...

Generalized complex geometry and supersymmetric non - linear sigma models

After an elementary presentation of the relation between supersymmetric nonlinear sigma models and geometry, I focus on 2D and the target space geometry allowed when there is an extra supersymmetry. This leads to a brief introduction to generalized complex geometry, a notion introduced recently by Hitchin which interpolates between complex and symplectic manifolds. Finally I present worldsheet ...

Incremental Spherical Linear Interpolation

Animation is often done by setting up a sequence of key orientations, represented by quaternions. The in between orientations are obtained by spherical linear interpolation (SLERP) of the quaternions, which then can be used to rotate the objects. However, SLERP involves the computation of trigonometric functions, which are computationally expensive. Since it is often required that the angle bet...