Abstract: Compliant foil gas lubricated bearings are used for the
support of light loads in the order of few kilograms at high speeds, in
the order of 50,000 RPM. The stiffness of the foil bearings depends
both on the stiffness of the compliant foil and on the lubricating
gas film. The stiffness of the bearings plays a crucial role in the
stable operation of the supported rotor over a range of speeds. This
paper describes a numerical approach to estimate the stiffness of the
bearings using pseudo spectral scheme. Methodology to obtain the
stiffness of the foil bearing as a function of weight of the shaft is
given and the results are presented.
Abstract: The optimization and control problem for 4D trajectories
is a subject rarely addressed in literature. In the 4D navigation
problem we define waypoints, for each mission, where the arrival
time is specified in each of them. One way to design trajectories for
achieving this kind of mission is to use the trajectory optimization
concepts. To solve a trajectory optimization problem we can use
the indirect or direct methods. The indirect methods are based on
maximum principle of Pontryagin, on the other hand, in the direct
methods it is necessary to transform into a nonlinear programming
problem. We propose an approach based on direct methods with a
pseudospectral integration scheme built on Chebyshev polynomials.
Abstract: In this paper we study some numerical methods to solve a model one-dimensional convection–diffusion equation. The semi-discretisation of the space variable results into a system of ordinary differential equations and the solution of the latter involves the evaluation of a matrix exponent. Since the calculation of this term is computationally expensive, we study some methods based on Krylov subspace and on Restrictive Taylor series approximation respectively. We also consider the Chebyshev Pseudospectral collocation method to do the spatial discretisation and we present the numerical solution obtained by these methods.
Abstract: This paper presents the use of Legendre pseudospectral
method for the optimization of finite-thrust orbital transfer for
spacecrafts. In order to get an accurate solution, the System-s
dynamics equations were normalized through a dimensionless method.
The Legendre pseudospectral method is based on interpolating
functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This
is used to transform the optimal control problem into a constrained
parameter optimization problem. The developed novel optimization
algorithm can be used to solve similar optimization problems of
spacecraft finite-thrust orbital transfer. The results of a numerical
simulation verified the validity of the proposed optimization method.
The simulation results reveal that pseudospectral optimization method
is a promising method for real-time trajectory optimization and
provides good accuracy and fast convergence.
Abstract: The projection methods, usually viewed as the methods
for computing eigenvalues, can also be used to estimate pseudospectra.
This paper proposes a kind of projection methods for computing
the pseudospectra of large scale matrices, including orthogonalization
projection method and oblique projection method respectively. This
possibility may be of practical importance in applications involving
large scale highly nonnormal matrices. Numerical algorithms are
given and some numerical experiments illustrate the efficiency of
the new algorithms.