Mass Matrix Inversion and AB Forward Dynamics

2010 ◽  
pp. 115-131
Author(s):  
Abhinandan Jain
Keyword(s):  
Mass Matrix ◽  
Matrix Inversion ◽  
Forward Dynamics

Closed Form Solutions to the Equation of Motion Avoiding Mass Matrix Inversion and Eigenvectors Decomposition

2001 ◽  
Author(s):  
Karine Reaud ◽  
Claude Vallee ◽  
Danielle Fortune
Keyword(s):  
Closed Form ◽  
Mass Matrix ◽  
Equation Of Motion ◽  
Matrix Inversion ◽  
Matrix Exponential ◽  
Linear Case ◽  
Closed Form Solutions ◽  
Damping Matrix ◽  
Ill Conditioned Matrices ◽  
Damping Systems

Abstract Solutions of the vibrations equations are generally obtained, in the linear case, by methods involving either matrix exponential computation or matrix eigendecomposition. However, these methods lead to a loss of symmetry because of the necessary inversion of the mass matrix. In doing so, one can introduce ill-conditioned matrices and, thus, compute eigenvectors with poor accuracy. In order to avoid these inconveniences, our method, which is an extension of Le Verrier-Souriau algorithm, provides solutions to the vibrations equations without inverting the mass matrix or computing eigenvectors. Moreover, we can solve damping systems even when the damping matrix has no specific properties such as the Basile property.

scholarly journals A Simulation of the Effects of Badminton Serve Release Height

2021 ◽  
Vol 11 (7) ◽  
pp. 2903
Author(s):  
John Rasmussen ◽  
Mark de Zee
Keyword(s):  
Experimental Data ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
World Federation ◽  
Forward Dynamics ◽  
Dynamics Model ◽  
Rib Cage ◽  
Female Player ◽  
Ballistic Trajectory ◽  
Release Height

In this work, we develop and calibrate a model to represent the trajectory of a badminton shuttlecock and use it to investigate the influence of serve height in view of a new serve rule instated by the Badminton World Federation. The new rule means that all players must launch the shuttlecock below a height of 1.15 m, as opposed to the old rule whereby the required launch height was under the rib cage of the server. The model is based on a forward dynamics model of ballistic trajectory with drag, and it is calibrated with experimental data. The experiments also served to determine the actual influence of the new rule on the shuttlecock launch position. The model is used in a Monte Carlo simulation to determine the statistical influence of the new serve rules on the player’s ability to perform good serves; i.e., serves with little opportunity for the receiver to attack. We conclude that, for the female player in question, serving below a height of 1.15 m makes it marginally more difficult to perform excellent serves. We also conclude that there might be alternative launch positions that would be less likely to produce the best serves but could be exploited as a tactical option.

scholarly journals Augmented Lagrangian preconditioners for the Oseen–Frank model of nematic and cholesteric liquid crystals

2021 ◽  
Author(s):  
Jingmin Xia ◽  
Patrick E. Farrell ◽  
Florian Wechsung
Keyword(s):  
Liquid Crystals ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Mass Matrix ◽  
Unit Length ◽  
Mesh Size ◽  
Schur Complement ◽  
Cholesteric Liquid Crystals ◽  
Multigrid Algorithm ◽  
The Cost

AbstractWe propose a robust and efficient augmented Lagrangian-type preconditioner for solving linearizations of the Oseen–Frank model arising in nematic and cholesteric liquid crystals. By applying the augmented Lagrangian method, the Schur complement of the director block can be better approximated by the weighted mass matrix of the Lagrange multiplier, at the cost of making the augmented director block harder to solve. In order to solve the augmented director block, we develop a robust multigrid algorithm which includes an additive Schwarz relaxation that captures a pointwise version of the kernel of the semi-definite term. Furthermore, we prove that the augmented Lagrangian term improves the discrete enforcement of the unit-length constraint. Numerical experiments verify the efficiency of the algorithm and its robustness with respect to problem-related parameters (Frank constants and cholesteric pitch) and the mesh size.

scholarly journals The singly-charged scalar singlet as the origin of neutrino masses

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Tobias Felkl ◽  
Juan Herrero-García ◽  
Michael A. Schmidt
Keyword(s):  
Mass Matrix ◽  
Boson Mass ◽  
Neutrino Masses ◽  
Charged Scalar ◽  
Yukawa Couplings ◽  
Left Handed ◽  
Flavour Violation ◽  
Singly Charged ◽  
Charged Lepton Sector ◽  
Scalar Singlet

Abstract We consider the generation of neutrino masses via a singly-charged scalar singlet. Under general assumptions we identify two distinct structures for the neutrino mass matrix. This yields a constraint for the antisymmetric Yukawa coupling of the singly-charged scalar singlet to two left-handed lepton doublets, irrespective of how the breaking of lepton-number conservation is achieved. The constraint disfavours large hierarchies among the Yukawa couplings. We study the implications for the phenomenology of lepton-flavour universality, measurements of the W-boson mass, flavour violation in the charged-lepton sector and decays of the singly-charged scalar singlet. We also discuss the parameter space that can address the Cabibbo Angle Anomaly.

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