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ij], suggests to identify local bases (11) and (13), intrinsically related to the physical properties of medium, with (22) and (23) of the just described arbitrary curvilinear coordinates system.
This paper introduces the solution of the Poisson problem in a certain type of curvilinear coordinate domain and points out problems with it.
Equation 13 provides an elegant general formulation of the equation of virtual work in curvilinear coordinates.
Gordon, "A Three-dimensional FDTD Algorithm in Curvilinear Coordinates," IEEE Transactions Antennas Propagation, Vol.
He explains the action approach, including its relation to Maxwell's equation and Dirac fields, then examines continuous symmetries and conservation laws, magnetostatics, multivalued fields in superfluids and superconductors, magnetic monopoles, electric charge confinement, multivalued mapping from ideal crystals to crystals with defects, defect melting, relativistic mechanics in curvilinear coordinates, torsion and curvature from defects and embedding, mutivalued mapping, field equations of gravitation, fields of integer spin, particles with half-integer spins, covariant conservation gravitation of spinning matter as a gauge theory, evanescent properties of torsion in gravity, the teleparallel theory of gravitation embedding, and emerging gravity.
A finite element method is developed from application of the principle of virtual work for the beam written in curvilinear coordinates in order to include the effects of finite deformation.