His topics include basis vectors and scale factors, contravarient components and transformations, metric tensor operation on tensor indices, Cartesian tensor
transformation--rotations, and a collection of relations for selected coordinate systems.
(1) Modeling the FOD function by symmetric cartesian tensor of order d and dimension 3.
Stella Atkins, "Symmetric positive semi-definite cartesian tensor fiber orientation distributions (CT-FOD)," Medical Image Analysis, vol.
(11.) Applequist, J., "Traceless cartesian tensor
forms for spherical harmonic functions: New theorems and applications to electrostatics of dielectric media," J.
Then the normal component of the Cartesian tensor
[sigma] on that plane is, using the summation convention over repeated indices:
Snider explains the Irreducible Cartesian Tensor
model that he and J.
Coverage includes the basic operations of vectors, matrices, Cartesian tensors
, domain and boundary surface integrals, kinematics, kinetics, linear elasticity, and Newtonian fluid mechanics, followed by chapters on curvilinear, nonlinear, electromagnetic, and differential geometry continuum.
As the text progresses, the author uses Cartesian tensors
to develop the theory of thermo-elasticity, the theory of generalized plane stress, and complex variable analysis.
A big advantage of co-rotational constitutive equations is that only Cartesian tensors
First, he deals with invariant modeling of flight dynamics, laying out the mathematical foundations of modeling with Cartesian tensors
, matrices, and coordinate systems.
Applied cartesian tensors
for aerospace simulations.