Motion and Vibration Analysis of a Roller Coaster

2001 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Tetsuya Kimura ◽  
Yoshinori Yamamoto
Keyword(s):  
Vibration Analysis ◽  
Simulation Analysis ◽  
Equation Of Motion ◽  
Differential Algebraic Equations ◽  
Parameter Variation ◽  
Algebraic Equations ◽  
Roller Coaster

Abstract Motion and vibration analysis of a roller coaster running in a 3D trajectory is carried out. The equation of motion of the roller coaster is derived in which the restriction in the trajectory is dealt with by using differential-algebraic equations (DAE) method. The effects of a parameter variation of the roller coaster to the vibration of the passenger are investigated in simulation analysis. The simulation result shows that when the parameter associated with the stiffness of the wheels of the roller coaster decreases, the passenger’s vibration increased. In addition, it shows that the discontinuity of the rate of increment of the trajectory induces large vibration.

A Hamiltonian Equation of Motion for Realtime Vehicle Simulation

1990 ◽  
Author(s):  
D. S. Bae ◽  
Y. S. Won
Keyword(s):  
Equations Of Motion ◽  
Transformation Method ◽  
Equation Of Motion ◽  
Differential Algebraic Equations ◽  
Coordinate Space ◽  
Hamiltonian Equation ◽  
Algebraic Equations ◽  
Vehicle Simulation ◽  
Relative Coordinate ◽  
New Formulation

Abstract A relative coordinate formulation of the Hamiltonian equation of motion is derived for realtime vehicle simulation. The Baumgarte stabilization method [1] is adopted to solve the Differential-Algebraic Equations (DAE) of motion. The stability theory of multi-step integration methods is used to determine the stabilization constant. The equations of motion are first derived in Cartesian space and are reduced to relative coordinate space using the velocity transformation method [2]. Partial derivative of the kinetic energy with respect to the relative coordinate is obtained from equivalence of the Lagrangian and the Newton-Euler formulations. Parallel processing of the formulation is also discussed. Realtime simulation of a passenger vehicle is carried out to demonstrate the efficiency of the new formulation.

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

Construction of Inverse System for Nonlinear Differential-algebraic Equations Subsystems

2009 ◽  
Vol 35 (8) ◽  
pp. 1094-1100 ◽  
Author(s):  
Xian-Zhong DAI ◽  
Qiang ZANG ◽  
Kai-Feng ZHANG
Keyword(s):  
Differential Algebraic Equations ◽  
Inverse System ◽  
Algebraic Equations

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

scholarly journals Application of the spectral pseudo-inversion to solving Hermitian systems of differential–algebraic equations

2014 ◽  
Vol 260 ◽  
pp. 218-228
Author(s):  
Yu.M. Nechepurenko ◽  
G.V. Ovchinnikov ◽  
M. Sadkane
Keyword(s):  
Differential Algebraic Equations ◽  
Algebraic Equations
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