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NASA NTRS1990

Staggered solution procedures for multibody dynamics simulation

A computational procedure is presented for the direct integration of the multibody dynamical (MBD) equations with constraints. Numerical experiments conducted with this MBD procedure indicate that it yields robust solutions in cases where the step size furnishes more than 20 samples for the period of highest apparent response frequency in a given multibody system. The MBD solution procedure is implemented in two separate modules: the generalized coordinated solver, 'CINT', and the constraint Lagrange multiplier solver, 'LINT'.

Park, K. C.↗

NASA NTRS1990

Explicit-implicit staggered procedure for multibody dynamics analysis

An explicit-implicit staggered time-integration procedure is presented for the solution of multibody dynamical equations involving large rotations and constraints. The algorithms adopts a two-stage modification of the central difference algorithm for integrating the translational coordinates and the angular velocity vector, and the midpoint implicit algorithm to solve the kinematical relation in terms of the Euler parameters for updating the angular orientations. The Lagrange multipliers to enforce the system constraints are obtained by implicitly integrating a parabolically regularized differential equation for the multipliers. The performance of the present procedure has been evaluated to applying the procedure to solve several sample problems. The results indicate that the procedure is robust in dealing with a variety of constraints and spatial kinematic motions, hence it is recommended for applications to general multibody dynamics analyses.

Park, K. C.↗

NASA NTRS1992

Effect of planform and body on supersonic aerodynamics of multibody configurations

An experimental and theoretical investigation of the effect of the wing planform and bodies on the supersonic aerodynamics of a low-fineness-ratio, multibody configuration has been conducted in the Langley Unitary Plan Wind Tunnel at Mach numbers of 1.60, 1.80, 2.00, and 2.16. Force and moment data, flow-visualization data, and surface-pressure data were obtained on eight low-fineness-ratio, twin-body configurations. These configurations varied in inboard wing planform shape, outboard wing planform shape, outboard wing planform size, and presence of the bodies. The force and moment data showed that increasing the ratio of outboard wing area to total wing area or increasing the leading-edge sweep of the inboard wing influenced the aerodynamic characteristics. The flow-visualization data showed a complex flow-field system of shocks, shock-induced separation, and body vortex systems occurring between the side bodies. This flow field was substantially affected by the inboard wing planform shape but minimally affected by the outboard wing planform shape. The flow-visualization and surface-pressure data showed that flow over the outboard wing developed as expected with changes in angle of attack and Mach number and was affected by the leading-edge sweep of the inboard wing and the presence of the bodies. Evaluation of the linear-theory prediction methods revealed their general inability to consistently predict the characteristics of these multibody configurations.

Mcmillin, S. Naomi↗

NASA NTRS1992

Planar reorientation maneuvers of space multibody systems using internal controls

In this paper a reorientation maneuvering strategy for an interconnection of planar rigid bodies in space is developed. It is assumed that there are no exogeneous torques, and torques generated by joint motors are used as means of control so that the total angular momentum of the multibody system is a constant, assumed to be zero in this paper. The maneuver strategy uses the nonintegrability of the expression for the angular momentum. We demonstrate that large-angle maneuvers can be designed to achieve an arbitrary reorientation of the multibody system with respect to an inertial frame. The theoretical background for carrying out the required maneuvers is briefly summarized. Specifications and computer simulations of a specific reorientation maneuver, and the corresponding control strategies, are described.

Reyhanoglu, Mahmut↗

NASA NTRS1993

A residual flexibility approach to multibody dynamics

Many complex systems can be modeled as a collection of interacting bodies, where the relative motion of the bodies may be large. The dynamics of such systems are simulated using multibody dynamic formulations. Many of these treat each body as a rigid component, but recently the flexibility of the components has been incorporated. This paper presents a residual flexibility formulation of the multibody dynamics problem. The formulation is very simple and offers great computational efficiency since it treats each body as a free structure in space, interacting with other bodies only through interface forces. Each body's accelerations can be solved independently, as can each set of interface forces. We have applied the technique successfully to several special applications, and the initial implementation in a general mechanisms code has given excellent results in comparison to a direct finite element representation of flexibility.

Blelloch, Paul A.↗

NASA NTRS1993

Recursive dynamics algorithm for multibody systems with prescribed motion

This paper uses spatial operator techniques to develop a new algorithm for the dynamics of multibody systems with hinges undergoing prescribed motion. This algorithm is spatially recursive, and its computational complexity grows only linearly with the number of degrees of freedom in the system. Its structure is a hybrid of known recursive forward and inverse dynamics algorithms for regular multibody systems. Changes to the prescribed/nonprescribed nature of hinges can be implemented during run time since they are handled with very low overhead in the algorithm.

Jain, Abhinandan↗

NASA NTRS1993

Assumed modes method and flexible multibody dynamics

The use of assumed modes in flexible multibody dynamics algorithms requires the evaluation of several domain dependent integrals that are affected by the type of modes used. The implications of these integrals - often called zeroth, first and second order terms - are investigated in this paper, for arbitrarily shaped bodies. Guidelines are developed for the use of appropriate boundary conditions while generating the component modal models. The issue of whether and which higher order terms must be retained is also addressed. Analytical results, and numerical results using the Shuttle Remote Manipulator System as the multibody system, are presented to qualitatively and quantitatively address these issues.

Tadikonda, S. S. K.↗

NASA NTRS1993

Hybrid equations of motion for flexible multibody systems using quasi-coordinates

A variety of engineering systems, such as automobiles, aircraft, rotorcraft, robots, spacecraft, etc., can be modeled as flexible multibody systems. The individual flexible bodies are in general characterized by distributed parameters. In most earlier investigations they were approximated by some spatial discretization procedure, such as the classical Rayleigh-Ritz method or the finite element method. This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates. Moreover, the equations for the elastic motions include rotatory inertia and shear deformation effects. The hybrid set is cast in state form, thus making it suitable for control design.

Meirovitch, L.↗

NASA NTRS1993

Geometric stiffening in multibody dynamics formulations

In this paper we discuss the issue of geometric stiffening as it arises in the context of multibody dynamics. This topic has been treated in a number of previous publications in this journal and appears to be a debated subject. The controversy revolves primarily around the 'correct' methodology for incorporating the stiffening effect into dynamics formulations. The main goal of this work is to present the different approaches that have been developed for this problem through an in-depth review of several publications dealing with this subject. This is done with the goal of contributing to a precise understanding of the existing methodologies for modelling the stiffening effects in multibody systems. Thus, in presenting the material we attempt to illuminate the key characteristics of the various methods as well as show how they relate to each other. In addition, we offer a number of novel insights and clarifying interpretations of these schemes. The paper is completed with a general classification and comparison of the different approaches.

Sharf, Inna↗

NASA NTRS1994

Computationally efficient multibody simulations

Computationally efficient approaches to the solution of the dynamics of multibody systems are presented in this work. The computational efficiency is derived from both the algorithmic and implementational standpoint. Order(n) approaches provide a new formulation of the equations of motion eliminating the assembly and numerical inversion of a system mass matrix as required by conventional algorithms. Computational efficiency is also gained in the implementation phase by the symbolic processing and parallel implementation of these equations. Comparison of this algorithm with existing multibody simulation programs illustrates the increased computational efficiency.

Ramakrishnan, Jayant↗

NASA NTRS1994

Numerical methods for multibody systems

This article gives a brief summary of some results obtained by Nasser on modeling and simulation of inequality problems in multibody dynamics. In particular, the augmented Lagrangian method discussed here is applied to a constrained motion problem with impulsive inequality constraints. A fundamental characteristic of the multibody dynamics problem is the lack of global convexity of its Lagrangian. The problem is transformed into a convex analysis problem by localization (piecewise linearization), where the augmented Lagrangian has been successfully used. A model test problem is considered and a set of numerical experiments is presented.

Glowinski, Roland↗

NASA NTRS1994

Mathematical modeling of a class of multibody flexible spacecraft structures

A mathematical model for a general multibody flexible spacecraft is obtained. The generic spacecraft considered consists of a flexible central body to which a number of flexible multibody structures are attached. The coordinate systems used in the derivation allow effective decoupling of the translational motion of the entire spacecraft from its rotational motion about its center of mass. The derivation assumes that the deformations in the bodies are only due to elastic motions. The dynamic model derived is a closed-form vector-matrix differential equation. The model developed can be used for analysis and simulation of many realistic spacecraft configurations.

Kelkar, Atul, G.↗

NASA NTRS1995

A class of stabilizing controllers for flexible multibody systems

The problem of controlling a class of nonlinear multibody flexible space systems consisting of a flexible central body to which a number of articulated appendages are attached is considered. Collocated actuators and sensors are assumed, and global asymptotic stability of such systems is established under a nonlinear dissipative control law. The stability is shown to be robust to unmodeled dynamics and parametric uncertainties. For a special case in which the attitude motion of the central body is small, the system, although still nonlinear, is shown to be stabilized by linear dissipative control laws. Two types of linear controllers are considered: static dissipative (constant gain) and dynamic dissipative. The static dissipative control law is also shown to provide robust stability in the presence of certain classes of actuator and sensor nonlinearities and actuator dynamics. The results obtained for this special case can also be readily applied for controlling single-body linear flexible space structures. For this case, a synthesis technique for the design of a suboptimal dynamic dissipative controller is also presented. The results obtained in this paper are applicable to a broad class of multibody and single-body systems such as flexible multilink manipulators, multipayload space platforms, and space antennas. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.

Joshi, Suresh M.↗

NASA NTRS2003

Multibody Parachute Flight Simulations for Planetary Entry Trajectories Using "Equilibrium Points"

A method has been developed to reduce numerical stiffness and computer CPU requirements of high fidelity multibody flight simulations involving parachutes for planetary entry trajectories. Typical parachute entry configurations consist of entry bodies suspended from a parachute, connected by flexible lines. To accurately calculate line forces and moments, the simulations need to keep track of the point where the flexible lines meet (confluence point). In previous multibody parachute flight simulations, the confluence point has been modeled as a point mass. Using a point mass for the confluence point tends to make the simulation numerically stiff, because its mass is typically much less that than the main rigid body masses. One solution for stiff differential equations is to use a very small integration time step. However, this results in large computer CPU requirements. In the method described in the paper, the need for using a mass as the confluence point has been eliminated. Instead, the confluence point is modeled using an "equilibrium point". This point is calculated at every integration step as the point at which sum of all line forces is zero (static equilibrium). The use of this "equilibrium point" has the advantage of both reducing the numerical stiffness of the simulations, and eliminating the dynamical equations associated with vibration of a lumped mass on a high-tension string.

Raiszadeh, Ben↗

NASA NTRS2004

Further Results of Soft-Inplane Tiltrotor Aeromechanics Investigation Using Two Multibody Analyses

This investigation focuses on the development of multibody analytical models to predict the dynamic response, aeroelastic stability, and blade loading of a soft-inplane tiltrotor wind-tunnel model. Comprehensive rotorcraft-based multibody analyses enable modeling of the rotor system to a high level of detail such that complex mechanics and nonlinear effects associated with control system geometry and joint deadband may be considered. The influence of these and other nonlinear effects on the aeromechanical behavior of the tiltrotor model are examined. A parametric study of the design parameters which may have influence on the aeromechanics of the soft-inplane rotor system are also included in this investigation.

Masarati, Pierangelo↗

NASA NTRS2005

A Unifying Multibody Dynamics Algorithm Development Workbench

The development of new and efficient algorithms for multibody dynamics has been an important research area. These algorithms are used for modeling, simulation, and control of systems such as spacecraft, robotic systems, automotive applications, the human body, manufacturing operations, and micro-electromechanical systems (MEMS). At JPL's Dynamics and Real Time Simulation (DARTS) Laboratory we have developed software that serves as a computational workbench for these algorithms. This software utilizes the mathematical perspective of the spatial operator algebra, which allows the development of dynamics algorithms and new insights into multibody dynamics.

Ziegler, John L.↗

NASA NTRS2009

Validation of Multibody Program to Optimize Simulated Trajectories II Parachute Simulation with Interacting Forces

A capability to simulate trajectories of multiple interacting rigid bodies has been developed, tested and validated. This capability uses the Program to Optimize Simulated Trajectories II (POST 2). The standard version of POST 2 allows trajectory simulation of multiple bodies without force interaction. In the current implementation, the force interaction between the parachute and the suspended bodies has been modeled using flexible lines, allowing accurate trajectory simulation of the individual bodies in flight. The POST 2 multibody capability is intended to be general purpose and applicable to any parachute entry trajectory simulation. This research paper explains the motivation for multibody parachute simulation, discusses implementation methods, and presents validation of this capability.

Raiszadeh, Behzad↗

NASA NTRSDate not supplied

A Flexible Multibody Approach to Space Launch System Liftoff Pad Separation with Umbilical Disconnect

A flexible multibody dynamic framework is applied to the Space Launch System(SLS)liftoff Coupled Loads Analysis(CLA), enabling computational efficiencies and systematic inclusion of component nonlinearities. This work simulates the SLS liftoff transient pad separation event inclusive of umbilical disconnects and preload strain energy release (twang). For this system level nonlinear dynamic simulation, the flexible multibody framework provides a systematic approach for the addition of component specific algorithms to enforce the subject nonlinearities. As such, the complexities associated with the nonlinear CLA are greatly reduced, facilitating simplified bookkeeping as well as accelerating the execution of the nonlinear time-domain simulations.

Joel W Sills↗