MBSymba swMATH ID: 4274 Software Authors: Lot, R.; Da Lio, M. Description: A symbolic approach for automatic generation of the equations of motion of multibody systems This paper describes a collection of methods and procedures for the automatic generation of the equations of motion of multibody systems using general-purpose Computer Algebra Software. A brief review of existing symbolic multibody systems is given, and advantages and disadvantages of symbolic approaches compared with numerical ones are discussed. Then, a set of methods for symbolic modeling of multibody systems is explained. The first step of the modeling procedure consists of the description of the multibody system, by defining objects (such as points, vectors, rigid bodies, forces and torques, special objects) and the relationships between them (kinematic chains, constraints). The second step is the derivation of the equations of motion, which can be performed in a quasiautomatic way. A further step is the linearization of the equations and the calculation of the system’s frequency response functions. By way of example, a dynamic model of the motorcycle is developed, obtaining the nonlinear equations of motion in a dependent coordinates’ formulation. Next, the equations of motion are linearized and reduced to an independent formulation, reobtaining the well known Sharp’s model of the straight running of the motorcycle. Root loci and frequency response functions are also calculated. This example demonstrates the power of the given symbolic procedures and shows how a model suitable for stability, handling and control analysis can be developed quickly and easily. The procedure described in this paper has been implemented in a Maple package called MBSymba, which is available on the web page www.dim.unipd.it/lot/mbsymba.html. Homepage: http://www.multibody.net/mbsymba/ Dependencies: Maple Keywords: stability; Maple package ’MBSymba’; motorcycle; second-order Lagrange equations Related Software: Maple; RODAS; SOCS; GEE; Python; CasADi; Ipopt; ACADO; AnyBody; SPACAR; BCCG+FAI; Simulink; CONTACT; DASSL; AUTO; MEXX; veDYNA; MATLAB ODE suite; ode23s; ode113 Cited in: 12 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A symbolic approach for automatic generation of the equations of motion of multibody systems. Zbl 1124.70002Lot, R.; Da Lio, M. 2004 all top 5 Cited by 29 Authors 3 Lot, Roberto 2 Cossalter, Vittore 2 Massaro, Matteo 2 Shafei, A. M. 2 Shafei, H. R. 1 Bartali, L. 1 Blanchette, Carl 1 Boisvert, Maxime 1 Bruni, Stefano 1 Carpinelli, Mariano 1 Da Lio, Mauro 1 Desmet, Wim 1 Desrochers, Alain 1 Gabiccini, Marco 1 Gubitosa, Marco 1 Guiggiani, Massimo 1 Joubert, Nicolas 1 Keppler, Rainer 1 Meijaard, Jacob Philippus 1 Mundo, Domenico 1 Pei, YongChen 1 Rancourt, Denis 1 Rill, Georg 1 Schwab, A. L. 1 Seemann, Wolfgang 1 St-Amant, Yves 1 Sun, YouHong 1 Van Khang, Nguyen 1 Wang, Jixin Cited in 3 Serials 8 Multibody System Dynamics 3 Meccanica 1 Mechanics Research Communications Cited in 5 Fields 11 Mechanics of particles and systems (70-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) Citations by Year