In this paper, an algorithm is proposed to avoid singularity associated with the most famous minimum element attitude parametrization, Euler angle set. The proposed algorithm makes use of the method of sequential rotation to avoid singularity associated with Euler angle set. Further, a switching algorithm is also proposed to switch between different Euler angle sets to avoid the singularity whi...

Modern attitude and heading reference systems (AHRS) generally use Kalman Filter to integrate gyros with some other augmenting sensors, such as accelerometers and magnetometers, to provide a long term stable orientation solution. The construction of the Kalman Filter for the AHRS is flexible, while the general options are the methods based on quaternion, Euler angles, or Euler angle errors. But...

OBJECTIVE To apply the dual Euler angles method to investigate the passive motion characteristics of the human ankle joint complex. DESIGN Three-dimensional kinematic data of the ankle joint complex was collected from 10 knee-below foot cadaver specimens. BACKGROUND Besides the Euler angles and screw axis methods, the dual Euler angles method has been proposed as an alternative approach to ...

We present a convergence analysis for the implicit-explicit (IMEX) Euler discretization of nonlinear evolution equations. The governing vector field of such an equation is assumed to be the sum of an unbounded dissipative operator and a Lipschitz continuous perturbation. By employing the theory of dissipative operators on Banach spaces, we prove that the IMEX Euler and the implicit Euler scheme...

We show that a mechanical model of a pin-jointed linked structure is exactly equivalent to a symplectic Euler discretisation of a Hamiltonian ODE system. The step-size of this discretisation relates to a mechanical quantity which can take arbitrary values. Thus we may explore the behaviour of the symplectic Euler method in regions not normally considered appropriate for a numerical scheme and i...

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor fiowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid ...

This paper proposes and analyzes two fully discrete mixed interior penalty discontinuous Galerkin (DG) methods for the fourth order nonlinear Cahn-Hilliard equation. Both methods use the backward Euler method for time discretization and interior penalty discontinuous Galerkin methods for spatial discretization. They differ from each other on how the nonlinear term is treated, one of them is bas...

Area-proportional Euler diagrams have many applications, for example they are often used for visualizing data in medical and biological domains. There have been a number of recent research efforts to automatically draw Euler diagrams when the areas of the regions are not considered, leading to a range of different drawing techniques. By contrast, substantially less progress has been made on the...

We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann–Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank...

A method is described for calibrating the Euler angles of a kinematic Kelvin clamp in order to absolutely calibrate the orientation of an instrument. This paper covers a method for calibrating all three Euler angles, with an emphasis on the rotation about the vertical axis. This method uses a fixture employing a theodolite with an autocollimating eyepiece and an autocollimating prism.