By minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. This new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. Since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. In fac...

The motion rotors, or motors, are used to model Euclidean motion in 3D conformal geometric algebra. In this chapter we present a technique for estimating the motor which best transforms one set of noisy geometric objects onto another. The technique reduces to an eigenrotator problem and has some advantages over matrix formulations. It allows motors to be estimated from a variety of geometric da...

We discuss in the paper the use of the Riemannian mean given by the differential geometric tools. This geometric mean is used in this paper for computing the class centers in the polarimetric H/α unsupervised classification process. We show that the class centers remain more stable during the iteration process, leading to a different interpretation of the H/α/A classification. This technique ca...

by minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. this new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. in fact, bot...

The paper proposes a very straightforward change of the general layout of the geometric approach to the feedforward and feedback model following problems for nonminimum-phase systems. The design technique relies on the replacement of the output matrix of the controlled system with an equally dimensioned matrix ensuring H2-optimality in the standard disturbance decoupling problem, while maintain...

We present a technique for evaluating classifications by geometric comparison of rule sets, Rules ~e represented as objects in an n-dimensional hyperspace. The similarity of classes is computed from the overlap of the geometric class descriptions, The system produces a correlation matrix that ̄ indicates the degree of similarity between each pair of classes. The technique can be applied to class...