scholarly journals An Extended Dynamical Equation of Motion, Phase Dependency and Inertial Backreaction

2017 ◽  
Author(s):  
Mario J. Pinheiro ◽  
◽  
Marcus Büker ◽  
Keyword(s):  
Dynamical Equation ◽  
Equation Of Motion

scholarly journals Modified Hamiltonian Formalism for Regge-Teitelboim Cosmology

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Pinaki Patra ◽  
Md. Raju ◽  
Gargi Manna ◽  
Jyoti Prasad Saha
Keyword(s):  
Cosmological Model ◽  
Tangent Bundle ◽  
Dynamical Equation ◽  
Hamiltonian Formalism ◽  
Equation Of Motion ◽  
Scale Factor ◽  
Correct Equation ◽  
Higher Derivative ◽  
Alternative Approach ◽  
Tangent Manifold

The Ostrogradski approach for the Hamiltonian formalism of higher derivative theory is not satisfactory because the Lagrangian cannot be viewed as a function on the tangent bundle to coordinate manifold. In this paper, we have used an alternative approach which leads directly to the Lagrangian which, being a function on the tangent manifold, gives correct equation of motion; no new coordinate variables need to be added. This approach can be used directly to the singular (in Ostrogradski sense) Lagrangian. We have used this method for the Regge-Teitelboim (RT) minisuperspace cosmological model. We have obtained the Hamiltonian of the dynamical equation of the scale factor of RT model.

The Effect of Oil Entrapment in an Axial Piston Pump

1985 ◽  
Vol 107 (4) ◽  
pp. 246-251 ◽  
Author(s):  
S. J. Lin ◽  
A. Akers ◽  
G. Zeiger
Keyword(s):  
Pressure Distribution ◽  
Dynamical Equation ◽  
Control Volume ◽  
Equation Of Motion ◽  
Piston Pump ◽  
Axial Piston Pump ◽  
Angular Rotation ◽  
Instantaneous Pressure ◽  
Discharge Pressure ◽  
Axial Piston

Values of pressure caused by entrapment beneath a valve plate have been calculated. The technique used consists of the solution of the dynamical equation of motion in the piston control volume. Instantaneous and average values of torque have also been deduced from the pressure distribution. Plots have been constructed showing the effect of swashplate angle, pump angular rotation, discharge pressure, and entrapment angle upon instantaneous pressure, torque, and average torque for a typical axial piston pump.

scholarly journals Concise method to the dynamic modeling of climbing robot

2017 ◽  
Vol 9 (2) ◽  
pp. 168781401769167 ◽  
Author(s):  
Yaru Xu ◽  
Rong Liu
Keyword(s):  
Numerical Method ◽  
Dynamic Modeling ◽  
Dynamic Equation ◽  
Dynamical Equation ◽  
Lagrange Equation ◽  
Equation Of Motion ◽  
Climbing Robot ◽  
Explicit Equation ◽  
Cavity Structure ◽  
The Given

With the aim of dynamic modeling of the climbing robot with dual-cavity structure and wheeled locomotion mechanism, a succinct and explicit equation of motion based on the Udwadia–Kalaba equation is established. The trajectory constraint of the climbing robot, which is regarded as the external constraint of the system, is integrated into the dynamic equation dexterously. A modified numerical method is considered to reduce the errors because the numerical results obtained by integrating the constrained dynamic equation yield the errors. The trajectories are almost coincident by comparing the modified numerical value and the theoretical value. The driving torques required to guarantee the climbing robot to move along the given trajectory are obtained explicitly, which overcomes the disadvantage of obtaining dynamical equation from traditional Lagrange equation by Lagrange multiplier. The simulations are performed to demonstrate that the dynamical equation established by this method with brevity and accuracy is in accordance with reality status.

Particle motion with air resistance

2012 ◽  
Vol 8 (1) ◽  
pp. 1-15
Author(s):  
Gy. Sitkei
Keyword(s):  
Basic Equation ◽  
Initial Conditions ◽  
Equation Of Motion ◽  
Terminal Velocity ◽  
Dimensionless Form ◽  
Wood Industry ◽  
Acceptable Error ◽  
General Validity ◽  
Practical Applications ◽  
Air Resistance

Motion of particles with air resistance (e.g. horizontal and inclined throwing) plays an important role in many technological processes in agriculture, wood industry and several other fields. Although, the basic equation of motion of this problem is well known, however, the solutions for practical applications are not sufficient. In this article working diagrams were developed for quick estimation of the throwing distance and the terminal velocity. Approximate solution procedures are presented in closed form with acceptable error. The working diagrams provide with arbitrary initial conditions in dimensionless form of general validity.

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

On the Harmonic Oscillations for the Motion of a Dynamical System

2017 ◽  
Vol 13 (2) ◽  
pp. 4657-4670
Author(s):  
W. S. Amer
Keyword(s):  
Dynamical System ◽  
Numerical Solutions ◽  
Equation Of Motion ◽  
Parameter Method ◽  
Kutta Method ◽  
Small Parameter Method ◽  
Harmonic Oscillations ◽  
Pivot Point ◽  
Runge Kutta Method ◽  
High Consistency

This work touches two important cases for the motion of a pendulum called Sub and Ultra-harmonic cases. The small parameter method is used to obtain the approximate analytic periodic solutions of the equation of motion when the pivot point of the pendulum moves in an elliptic path. Moreover, the fourth order Runge-Kutta method is used to investigate the numerical solutions of the considered model. The comparison between both the analytical solution and the numerical ones shows high consistency between them.

A Multi-Layer Approach to the Equation of Motion Coupled-Cluster Method for the Electron Affinity

2020 ◽  
Author(s):  
Soumi Haldar ◽  
Achintya Kumar Dutta
Keyword(s):  
Electron Affinity ◽  
Electron Attachment ◽  
Equation Of Motion ◽  
Cluster Method ◽  
Coupled Cluster ◽  
Coupled Cluster Method ◽  
Large Molecules ◽  
Layer Method ◽  
Speed Up ◽  
Attachment Process

We have presented a multi-layer implementation of the equation of motion coupled-cluster method for the electron affinity, based on local and pair natural orbitals. The method gives consistent accuracy for both localized and delocalized anionic states. It results in many fold speedup in computational timing as compared to the canonical and DLPNO based implementation of the EA-EOM-CCSD method. We have also developed an explicit fragment-based approach which can lead to even higher speed-up with little loss in accuracy. The multi-layer method can be used to treat the environmental effect of both bonded and non-bonded nature on the electron attachment process in large molecules.<br>

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