Dynamic effects on atomic and molecular oxygen density distributions in the upper atmosphere: a numerical solution to equations of motion and continuity

1967 ◽  
Vol 29 (6) ◽  
pp. 723-747 ◽  
Author(s):  
Tatsuo Shimazaki
Keyword(s):  
Numerical Solution ◽  
Molecular Oxygen ◽  
Equations Of Motion ◽  
Upper Atmosphere ◽  
Dynamic Effects ◽  
Density Distributions

On the Parametric Excitation of Pendulum-Type Vibration Absorber

1961 ◽  
Vol 28 (3) ◽  
pp. 330-334 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Energy Transfer ◽  
Numerical Solution ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Vibration Absorber ◽  
Single Cycle ◽  
Linearized System ◽  
Nonlinear Equations Of Motion ◽  
Beam Oscillation ◽  
Energy Interchange

The free motion of an undamped pendulum-type vibration absorber is studied on the basis of approximate nonlinear equations of motion. It is shown that this type of mechanical system exhibits the phenomenon of auto parametric excitation; a type of “instability” which cannot be accounted for on the basis of the linearized system. Complete energy transfer between modes is shown to occur when the beam frequency is twice the simple pendulum frequency. On the basis of a numerical solution, approximately 150 cycles of the beam oscillation take place during a single cycle of energy interchange.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

An Approach for the Dynamics of Robotic Manipulators With Structural Flexibility of Links and Joints

1997 ◽  
Author(s):  
J. Kövecses ◽  
R. G. Fenton ◽  
W. L. Cleghorn
Keyword(s):  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Structural Flexibility ◽  
Flexible Link ◽  
Dynamic Effects ◽  
Flexible Joint ◽  
Modeling And Analysis ◽  
Discrete Parameter ◽  
Rigid Link ◽  
Different Types

Abstract In this paper, an approach is presented for the dynamic modeling and analysis of robotic manipulators having structural flexibility in the links and joints. The formulation allows the user to include different types of flexibilities, as required. This approach includes the dynamic effects of joint driving systems by considering the mass and moments of inertia of their elements, the rotor-link interactions, and the gear reduction ratios; all of which can have significant influences on the behavior of the manipulator. Both distributed-discrete and discretized-discrete parameter models of a robot can be analysed. In the discretized-discrete case, dynamic equations of motion are developed for four model types: rigid link - rigid joint, rigid link - flexible joint, flexible link - rigid joint, and flexible link - flexible joint. An example of a two-link manipulator is considered. Simulation results are presented for different models (flexible joint - rigid link, rigid joint - flexible link, flexible joint - flexible link) of the manipulator. The computations show the influence of joint and link flexibilities on the manipulator performance.

Propagation of Nonlinearities in the Inertia Matrix of Tracked Vehicles

1994 ◽  
Author(s):  
J. H. Choi ◽  
A. A. Shabana ◽  
Roger A. Wehage
Keyword(s):  
Numerical Solution ◽  
Vehicle Dynamics ◽  
Equations Of Motion ◽  
Coefficient Matrix ◽  
Influence Coefficient ◽  
Dynamic Force ◽  
Tracked Vehicles ◽  
Revolute Joints ◽  
Inertia Matrix ◽  
Force Coupling

Abstract In this investigation, a procedure is presented for the numerical solution of tracked vehicle dynamics equations of motion. Tracked vehicles can be represented as two kinematically decoupled subsystems. The first is the chassis subsystem which consists of chassis, rollers, idlers, and sprockets. The second is the track subsystem which consists of track links interconnected by revolute joints. While there is dynamic force coupling between these two subsystems, there is no inertia coupling since the kinematic equations of the two subsystems are not coupled. The objective of the procedure developed in this investigation is to take advantage of the fact that in many applications, the shape of the track does not significantly change even though the track links undergo significant configurations changes. In such cases the nonlinearities propagate along the diagonals of a velocity influence coefficient matrix. This matrix is the only source of nonlinearities in the generalized inertia matrix. A permutation matrix is introduced to minimize the number of generalized inertia matrix LU factor evaluations for the track.

Nitric oxide and molecular oxygen in the earth's upper atmosphere

1959 ◽  
Vol 1 (3) ◽  
pp. 161-172 ◽  
Author(s):  
A.S. Jursa ◽  
Y. Tanaka ◽  
F. LeBlanc
Keyword(s):  
Nitric Oxide ◽  
Molecular Oxygen ◽  
Upper Atmosphere

Atomistic Simulation of Vapor-Phase Nanoparticle Formation

1994 ◽  
Vol 351 ◽  
Author(s):  
Michael R. Zachariah ◽  
Michael J. Carrier ◽  
Estela Blaisten-Barojas
Keyword(s):  
Atomistic Simulation ◽  
Equations Of Motion ◽  
Stable State ◽  
Dynamic Effects ◽  
Diffusion Constants ◽  
Large Heat ◽  
Dynamics Simulations ◽  
Three Body ◽  
The Impact ◽  
Weber Potential

ABSTRACTIn order to understand from a fundamental view how nanoparticles form and grow, classical molecular dynamics simulations of cluster growth and energy accommodation processes have been conducted for clusters of silicon (< 1000 atoms), over a wide temperature range. Simulations involved solution of the classical equations of motion constrained with the three body Stillinger-Weber potential. The results show the large heat release and resulting cluster heating during a cluster-cluster collision event, and the corresponding time evolution of the internal energy to a more stable state. Dynamic effects associated with the temperature of the cluster and the impact parameter are also clearly evident. In particular, clusters show a large sensitivity to temperature in the rate of coalescence, particularly at low temperature. Calculated diffusion coefficients are significantly larger than surface diffusion constants stated in the literature. Phonon density of states spectra do not seem to show size effects.

A Simultaneous Numerical Solution for the Lubrication and Dynamic Stability of Noncontacting Gas Face Seals

2000 ◽  
Vol 123 (2) ◽  
pp. 388-394 ◽  
Author(s):  
Itzhak Green ◽  
Roger M. Barnsby
Keyword(s):  
Numerical Solution ◽  
Equations Of Motion ◽  
Critical Value ◽  
Pressure Drops ◽  
Mode 2 ◽  
Face Seals ◽  
Natural Response ◽  
The Stability ◽  
Film Lubrication ◽  
Fluid Film Lubrication

A numerical solution is presented for the dynamic analysis of gas lubricated noncontacting mechanical face seals having a single grounded flexibly mounted stator. Seal dynamics is solved in axial and angular modes of motion. Both the Reynolds equation and the equations of motion are arranged into a single state space form, allowing the fluid film lubrication and the dynamics to be solved simultaneously. The resulting set of equations is solved using a high-order multistep ordinary differential equation solver, yielding a complete simulation for the seal dynamic behavior. Examples of seal motion are given in detailed transient responses. The stability threshold is investigated to gauge the influence of seal parameters such as inertia, speed, coning, and the direction of sealed pressure drops. The results show two modes of instability: (1) When the inertia effect is larger than a critical value, the natural response of the seal grows monotonically in a half-frequency-whirl mode. (2) When the seal coning is less than some critical value in an outside pressurized seal, the minimum film thickness diminishes because of hydrostatic instability, and face contact occurs. Conversely, an inside pressurized seal is shown to be hydrostatically stable and have a superior dynamic response at any coning.

scholarly journals Quantum Cosmology of Quadratic f(R) Theories with a FRW Metric

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
V. Vázquez-Báez ◽  
C. Ramírez
Keyword(s):  
Wave Function ◽  
Scalar Field ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Quantum Cosmology ◽  
Free Parameter ◽  
Equations Of Motion ◽  
Frw Metric ◽  
The Universe

We study the quantum cosmology of a quadratic fR theory with a FRW metric, via one of its equivalent Horndeski type actions, where the dynamic of the scalar field is induced. The classical equations of motion and the Wheeler-DeWitt equation, in their exact versions, are solved numerically. There is a free parameter in the action from which two cases follow: inflation + exit and inflation alone. The numerical solution of the Wheeler-DeWitt equation depends strongly on the boundary conditions, which can be chosen so that the resulting wave function of the universe is normalizable and consistent with Hermitian operators.

The Discrete Adjoint Gradient Computation for Optimization Problems in Multibody Dynamics

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Thomas Lauß ◽  
Stefan Oberpeilsteiner ◽  
Wolfgang Steiner ◽  
Karin Nachbagauer
Keyword(s):  
Numerical Solution ◽  
Adjoint Method ◽  
Optimization Problems ◽  
Equations Of Motion ◽  
Adjoint System ◽  
Solution Procedure ◽  
Cost Functional ◽  
Discrete Adjoint ◽  
Discrete Adjoint Method ◽  
Stability And Accuracy

The adjoint method is a very efficient way to compute the gradient of a cost functional associated to a dynamical system depending on a set of input signals. However, the numerical solution of the adjoint differential equations raises several questions with respect to stability and accuracy. An alternative and maybe more natural approach is the discrete adjoint method (DAM), which constructs a finite difference scheme for the adjoint system directly from the numerical solution procedure, which is used for the solution of the equations of motion. The method delivers the exact gradient of the discretized cost functional subjected to the discretized equations of motion. For the application of the discrete adjoint method to the forward solver, several matrices are necessary. In this contribution, the matrices are derived for the simple Euler explicit method and for the classical implicit Hilber–Hughes–Taylor (HHT) solver.

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