In a previous paper [1] an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov’s volume formula for SU(N) [2,3] will also be derived. As an example of this parameterization’s usefulness, the density matrix paramete...

This paper proposes a globally optimal direct least squares (DLS) method for the PnP problem with Cayley parameterization. First we derive a new optimality condition without Lagrange multipliers, which is independent of any rotation representations. Then, we show that the new equation can be solved by several types of parameterizations and among them, Cayley parameterization is the most efficie...

Two classes of partially known systems are considered in this note; both of them have a fractional parameterization of the unknowns. The first class consists of nonlinear systems whose uncertainties are bounded by a function of fractional parameterization, and the second class compromises those systems whose unknown dynamics can directly, but nonlinearly, be parameterized. It is shown that adap...

Controller parameterization is a very fundamental problem in control theory. It provides an elegant and efficient way towards solving the stabilizing and design problem, with which all stabilizing controllers are characterized and thus a constrained design procedure can be replaced by an unconstrained optimization. In this paper we deal with the problem of characterizing all stabilizing control...

an enhanced displacement feedback structural control procedure is presented for performance-based design in this paper. at first, a comparative study is implemented assessing three most common active control algorithms including state, acceleration, and displacement feedback controls. the advantage of the displacement feedback algorithm for active control of structures against earthquakes is de...

For aerodynamic modeling and optimization, it is desirable to limit the number of design variables to reduce model complexity and the requirements of the applied optimization scheme. The Class/Shape Transformation (CST) surface parameterization method presented by Kulfan has proven to be particularly useful for this while maintaining a wide range of applications. These include everything from s...

The behavior of Catmull-Rom curves heavily depends on the choice of parameter values at the control points. We analyze a class of parameterizations ranging from uniform to chordal parameterization and show that, within this class, curves with centripetal parameterization contain properties that no other curves in this family possess. Researchers have previously indicated that centripetal parame...

Meshes obtained from laser scanner data often contain topological noise due to inaccuracies in the scanning and merging process. This topological noise complicates subsequent operations such as remeshing, parameterization and smoothing. We introduce an approach that removes unnecessary nontrivial topology from meshes. Using a local wave front traversal, we discover the local topologies of the m...

Numerical state-dependent Riccati equation based integrated guidance-control formulation is developed for an internally actuated missile. The dynamic system under consideration is of tenth order, making it tedious to algebraically manipulate the equations of motion into the state-dependent coefficient form central to the design methodology. A numerical approach based on previous research is dev...