In the case of complex multibody systems, an efficient and time-saving computation of the equations of motion is essential; in particular, concerning the inertia forces. When using the floating frame of reference formulation for modeling a multibody system, the inertia forces, which include velocity-dependent forces, depend nonlinearly on the system state and, therefore, have to be updated in each time step of the dynamic simulation. Since the emphasis of the present investigation is on the efficient computation of the velocity-dependent inertia forces as along with a fast simulation of multibody systems, a detailed derivation of the latter forces for the case of a general rotational parameterization is given. It has to be emphasized that the present investigations revealed a simpler representation of the velocity-dependent inertia forces compared to results presented in the literature. In contrast to the formulas presented in the literature, the presented formulas do not depend on the type of utilized rotational parameterization or on any associated assumptions.

References

References
1.
Shabana
,
A.
,
1997
, “
Flexible Multibody Dynamics: Review of Past and Recent Developments
,”
Multibody Syst, Dyn.
,
1
, pp.
189
222
.10.1023/A:1009773505418
2.
Wasfy
,
T.
, and
Noor
,
A.
,
2003
, “
Computational Strategies for Flexible Multibody Systems
,”
Appl. Mech. Rev.
,
56
(
6
), pp.
553
613
.10.1115/1.1590354
3.
Shabana
,
A.
,
1997
, “
Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation
,”
Multibody Syst. Dyn.
,
1
(
3
), pp.
339
348
.10.1023/A:1009740800463
4.
Géradin
,
M.
,
Robert
,
G.
, and
Bernardin
,
C.
,
1984
, “
Dynamic Modelling of Manipulators With Flexible Members
,”
Advanced Software in Robotics
,
A. D. M.
Géradin
, ed.,
Elsevier
,
New York
.
5.
Shabana
,
A.
,
2005
,
Dynamics of Multibody Systems
,
3rd ed.
,
Cambridge University Press
,
New York
.
6.
Veubeke
,
B.
,
1972
, “
A New Variational Principle for Finite Elastic Displacements
,”
Int. J. Eng. Sci.
,
10
, pp.
745
763
.10.1016/0020-7225(72)90079-1
7.
Simo
,
J.
,
1985
, “
A Finite Strain Beam Formulation. The Three-Dimensional Dynamic Problem. Part I
,”
Comput. Methods Appl. Mech. Eng.
,
49
, pp.
55
70
.10.1016/0045-7825(85)90050-7
8.
Ibrahimbegović
,
A.
,
1995
, “
On Finite Element Implementation of Geometrically Nonlinear Reissner's Beam Theory: Three-Dimensional Curved Beam Elements
,”
Comput. Methods Appl. Mech. Eng.
,
122
, pp.
11
26
.10.1016/0045-7825(95)00724-F
9.
Shabana
,
A.
,
2014
,
Dynamics of Multibody Systems
, (
4th ed.
,
Cambridge University Press
,
New York
.
10.
Schwertassek
,
R.
and
Wallrapp
,
O.
,
1999
,
Dynamik flexibler Mehrkörpersysteme
,
Vieweg
,
Braunschweig/Wiesbaden
.
11.
Lugris
,
U.
,
Naya
,
M.
,
Luaces
,
A.
, and
Cuadrado
,
J.
,
2009
, “
Efficient Calculation of the Inertia Terms in Floating Frame of Reference Formulations for Flexible Multibody Dynamics
,”
Proc. Inst. Mech. Eng., Part K: J. Multibody Dyn.
,
223
, pp.
147
157
.
12.
Pfister
,
J.
,
2006
, “
Elastic Multibody Systems With Frictional Contacts
,” Ph.D. dissertation, Universität Stuttgart, Stuttgart, Germany.
13.
Yoo
,
W. S.
, and
Haug
,
E. J.
,
1986
, “
Dynamics of Articulated Structures. Part I. Theory
,”
J. Struct. Mech.
,
14
(
1
), pp.
105
126
.10.1080/03601218608907512
14.
Diebel
,
J.
,
2006
, “
Representing Attitude: Euler Angles, Quaternions, and Rotation Vectors
,” Ph.D. dissertation, Stanford University, Palo Alto, CA.
15.
Schwab
,
A.
, and
Meijaard
,
J.
,
2006
, “
How to Draw Euler Angles and Utilize Euler Parameters
,”
Proceedings of the IDETC/CIE 2006, ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, Philadelphia, PA, Sept. 10–13, Paper No. DETC2006-99307, pp.
1
7
.
16.
Serban
,
R.
, and
Haug
,
E.
,
1998
, “
Analytical Derivatives for Multibody System Analyses
,”
Mech. Struct. Mach.
,
26
(
2
), pp.
145
173
.10.1080/08905459808945425
17.
Schaffer
,
A.
,
2005
, “
On the Adjoint Formulation of Design Sensitivity Analysis of Multibody Dynamics
,” Ph.D. dissertation, University of Iowa, Iowa City, IA.
18.
Roberson
,
R.
,
1985
, “
On the Practical Use of Euler-Rodriguez Parameters in Multibody System Dynamic Simulation
,”
Ingenieur-Archiv, Springer-Verlag
,
55
(
2
), pp.
114
123
.10.1007/BF00536828
19.
Shoemake
,
K.
,
1985
, “
Animating Rotation With Quaternion Curves
,”
Proceedings of SIGGRAPH 85
, New York, NY, pp.
245
254
.
20.
Soo Kim
,
M.
, and
Won Nam
,
K.
,
1995
, “
Interpolating Solid Orientations With Circular Blending Quaternion Curves
,”
Comput.-Aided Des.
,
27
, pp.
385
398
.10.1016/0010-4485(95)96802-S
21.
Betsch
,
P.
, and
Steinmann
,
P.
,
2002
, “
Frame-Indifferent Beam Finite Elements Based Upon the Geometrically Exact Beam Theory
,”
Int. J. Numer. Methods Eng.
,
54
, pp.
1775
1788
.10.1002/nme.487
22.
Likins
,
P.
,
1976
, “
Modal Method for Analysis of Free Rotations of Spacecraft
,”
AIAA J.
,
5
(
7
), pp.
1304
1308
.10.2514/3.4188
23.
Shabana
,
A.
,
1985
, “
Automated Analysis of Constrained Inertia-Variant Flexible Systems
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
,
107
(
4
), pp.
431
440
.10.1115/1.3269284
24.
Amirouche
,
F.
,
2006
,
Fundamentals of Multibody Dynamics: Theory and Applications
,
Birkhäuser
,
Boston, MA
.
25.
Pfeiffer
,
F.
,
2008
,
Mechanical System Dynamics (Lecture Notes in Applied and Computational Mechanics)
, Vol.
40
,
Springer-Verlag
,
Berlin/Heidelberg, Germany
.
26.
Ziegler
,
F.
,
1998
,
Mechanics of Solids and Fluids
,
2nd ed.
,
Springer
,
New York
.
27.
Parkus
,
H.
,
1995
,
Mechanik der festen Körper
,
2nd ed.
,
Springer
,
Vienna, Austria
.
28.
Pfeiffer
,
F.
,
1992
,
Einführung in die Dynamik
,
2nd ed.
,
Teubner
,
Stuttgart, Germany
.
You do not currently have access to this content.