Interactive Computerized Symbolic Dynamics for the Dynamicist

Schaechter, D. B.; Levinson, David A.

doi:10.23919/acc.1988.4789713

Cited by 16 publications

(18 citation statements)

References 26 publications

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“…To verify the POST2/CFE simulation results, a simulation was also created with AUTOLEV, [20][21][22] an interactive program designed specifically for the kinematic and dynamic analysis of mechanical systems. Symbolic manipulation (computer algebra) is used to formulate explicit equations of motion for the particular system of interest using any method; the software is particularly well suited to Kane's method.…”

Section: A Test Case I Fixed Jointmentioning

confidence: 99%

Verification of a Constraint Force Equation Methodology for Modeling Multi-Body Stage Separation

Tartabini

Roithmayr

Toniolo

et al. 2008

AIAA Modeling and Simulation Technologies Conference and Exhibit

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This paper discusses the verification of the Constraint Force Equation (CFE) methodology and its implementation in the Program to Optimize Simulated Trajectories II (POST2) for multibody separation problems using three specially designed test cases. The first test case involves two rigid bodies connected by a fixed joint; the second case involves two rigid bodies connected with a universal joint; and the third test case is that of Mach 7 separation of the Hyper-X vehicle. For the first two cases, the POST2/CFE solutions compared well with those obtained using industry standard benchmark codes, namely AUTOLEV and ADAMS. For the Hyper-X case, the POST2/CFE solutions were in reasonable agreement with the flight test data. The CFE implementation in POST2 facilitates the analysis and simulation of stage separation as an integral part of POST2 for seamless end-to-end simulations of launch vehicle trajectories.

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Section: A Test Case I Fixed Jointmentioning

confidence: 99%

Verification of a Constraint Force Equation Methodology for Modeling Multi-Body Stage Separation

Tartabini

Roithmayr

Toniolo

et al. 2008

AIAA Modeling and Simulation Technologies Conference and Exhibit

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“…One such symbolic package is Autolev [32] [16] and another is SymBody, a new toolbox for MATLAB r created by the authors and described in Section 5.5 below.…”

Section: Approaches To the Formulation And Simulation Of Systems Subjmentioning

confidence: 99%

“…Like Autolev, a symbolic manipulator written in C for dynamic system analysis [32], SymBody provides tailored data objects to describe components and geometric entities Equations of motion for a dynamic system are automatically generated using Kane's method once necessary kinematic and dynamic variables are defined by the user using an input script. Constraint equations can be embedded into equations of motion to obtain the minimal representation using the constrain command.…”

Section: Symbolic Manipulation In Matlab Rmentioning

confidence: 99%

On-Line Symbolic Constraint Embedding for Simulation of Hybrid Dynamical Systems

et al. 2005

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Abstract. In this paper we present a simulator designed to handle multibody systems with changing constraints, wherein the equations of motion for each of its constraint configurations are formulated in minimal ODE form with constraints embedded before they are passed to an ODE solver. The constraint-embedded equations are formulated symbolically according to a re-combination of terms of the unconstrained equations, and this symbolic process is undertaken on-line by the simulator.Constraint-embedding undertaken on-the-fly enables the simulation of systems with an ODE solver for which constraints are not known prior to simulation start or for which the enumeration of all constraint conditions would be unwieldy because of their complexity or number. Issues of drift associated with DAE solvers that usually require stabilization are sidestepped with the constraint-embedding approach. We apply nomenclature developed for hybrid dynamical systems to describe the system with changing constraints and to distinguish the roles of the forward dynamics solver, a collision detector, and an impact resolver. We have developed a MATLAB r toolbox for symbolically generating equations of motion using Kane's method and prototyped a simulator with on-line constraint embedding and demonstrated the design in three representative examples.

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“…Two well-known computer programs, discussed in Refs. [35], [36], and [37], employ computer algebra in carrying out Kane's method to derive equations of motion specific to the system of interest, and subsequently to create software for numerical solution of the equations.…”

Section: Equations Of Motion For Complex Nonholonomic Systemsmentioning

confidence: 99%

Forces associated with non-linear non-holonomic constraint equations

Roithmayr

Hodges

2010

International Journal of Non-Linear Mechanics

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A concise method has been formulated for identifying a set of forces needed to constrain the behavior of a mechanical system, modeled as a set of particles and rigid bodies, when it is subject to motion constraints described by nonholonomic equations that are inherently nonlinear in velocity. An expression in vector form is obtained for each force; a direction is determined, together with the point of application. This result is a consequence of expressing constraint equations in terms of dot products of vectors rather than in the usual way, which is entirely in terms of scalars and matrices. The constraint forces in vector form are used together with two new analytical approaches for deriving equations governing motion of a system subject to such constraints. If constraint forces are of interest they can be brought into evidence in explicit dynamical equations by employing the well-known nonholonomic partial velocities associated with Kane's method; if they are not of interest, equations can be formed instead with the aid of vectors introduced here as nonholonomic partial accelerations. When the analyst requires only the latter, smaller set of equations, they can be formed directly; it is not necessary to expend the labor to form the former, larger set first and subsequently perform matrix multiplications.

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Interactive Computerized Symbolic Dynamics for the Dynamicist

Cited by 16 publications

References 26 publications

Verification of a Constraint Force Equation Methodology for Modeling Multi-Body Stage Separation

Verification of a Constraint Force Equation Methodology for Modeling Multi-Body Stage Separation

On-Line Symbolic Constraint Embedding for Simulation of Hybrid Dynamical Systems

Forces associated with non-linear non-holonomic constraint equations

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