Poursina,
M.
,
Bhalerao,
K. D.
,
Flores,
S.
,
Anderson,
K. S.
, and
Laederach,
A.
, 2011, “
Strategies for Articulated Multibody-Based Adaptive Coarse Grain Simulation of RNA,” Methods Enzymol.,
487, pp. 73–98.

[PubMed]
Anderson,
K. S.
, 1990, “
Recursive Derivation of Explicit Equations of Motion for Efficient Dynamic/Control Simulation of Large Multibody Systems,” Ph.D. thesis, Stanford University, Stanford, CA.

Armstrong,
W. W.
, 1979, “
Recursive Solution to the Equations of Motion of an *n*-Link Manipulator,” Fifth World Congress on the Theory of Machines and Mechanisms, Vol.
2, pp. 1342–1346.

Bae,
D. S.
, and
Haug,
E. J.
, 1987, “
A Recursive Formation for Constrained Mechanical System Dynamics: Part I, Open Loop Systems,” Mech. Struct. Mach.,
15(3), pp. 359–382.

[CrossRef]
Brandl,
H.
,
Johanni,
R.
, and
Otter,
M.
, 1986, “
A Very Efficient Algorithm for the Simulation of Robots and Similar Multibody Systems Without Inversion of the Mass Matrix,” IFAC/IFIP/IMACS Symposium, pp. 95–100.

Featherstone,
R.
, 1983, “
The Calculation of Robotic Dynamics Using Articulated Body Inertias,” Int. J. Rob. Res.,
2(1), pp. 13–30.

[CrossRef]
Featherstone,
R.
, 1987, Robot Dynamics Algorithms,
Kluwer Academic Publishing, Norwell, MA.

Luh,
J. S. Y.
,
Walker,
M. W.
, and
Paul,
R. P. C.
, 1980, “
On-Line Computational Scheme for Mechanical Manipulators,” ASME J. Dyn. Syst. Meas. Control,
102(2), pp. 69–76.

[CrossRef]
Neilan,
P. E.
, 1986, “
Efficient Computer Simulation of Motions of Multibody Systems,” Ph.D. thesis, Stanford University, Stanford, CA.

Rosenthal,
D.
, 1990, “
An Order *n* Formulation for Robotic Systems,” J. Astronaut. Sci.,
38(4), pp. 511–529.

Rosenthal,
D. E.
, and
Sherman,
M. A.
, 1986, “
High Performance Multibody Simulations Via Symbolic Equation Manipulation and Kane's Method,” J. Astronaut. Sci.,
34(3), pp. 223–239.

Vereshchagin,
A. F.
, 1974, “
Computer Simulation of the Dynamics of Complicated Mechanisms of Robot-Manipulators,” Eng. Cybernet.,
12(6), pp. 65–70.

Walker,
M. W.
, and
Orin,
D. E.
, 1982, “
Efficient Dynamic Computer Simulation of Robotic Mechanisms,” ASME J. Dyn. Syst. Meas. Control,
104(3), pp. 205–211.

[CrossRef]
Sandu,
A.
,
Sandu,
C.
, and
Ahmadian,
M.
, 2006, “
Modeling Multibody Systems With Uncertainties. Part I: Theoretical and Computational Aspects,” Multibody Syst. Dyn.,
15(4), pp. 369–391.

[CrossRef]
Sandu,
C.
,
Sandu,
A.
, and
Ahmadian,
M.
, 2006, “
Modeling Multibody Systems With Uncertainties. Part II: Numerical Applications,” Multibody Syst. Dyn.,
15(3), pp. 241–262.

[CrossRef]
Murthy,
R.
,
El-Shafei,
A.
, and
Mignolet,
M.
, 2010, “
Nonparametric Stochastic Modeling of Uncertainty in Rotordynamics—Part I: Formulation,” ASME J. Eng. Gas Turbines Power,
132(9), p. 092501.

[CrossRef]
Murthy,
R.
,
El-Shafei,
A.
, and
Mignolet,
M.
, 2010, “
Nonparametric Stochastic Modeling of Uncertainty in Rotordynamics—Part II: Applications,” ASME J. Eng. Gas Turbines Power,
132(9), p. 092502.

[CrossRef]
Soize,
C.
, 2000, “
A Nonparametric Model of Random Uncertainties for Reduced Matrix Models in Structural Dynamics,” Probab. Eng. Mech.,
15(3), pp. 277–294.

[CrossRef]
Soize,
C.
, 2001, “
Maximum Entropy Approach for Modeling Random Uncertainties in Transient Elastodynamics,” J. Acoust. Soc. Am.,
109(5), pp. 1979–1996.

[CrossRef] [PubMed]
Batou,
A.
, and
Soize,
C.
, 2012, “
Rigid Multibody System Dynamics With Uncertain Rigid Bodies,” Multibody Syst. Dyn.,
27(3), pp. 285–319.

[CrossRef]
Ghanem,
R. G.
, and
Spanos,
P. D.
, 1991, Stochastic Finite Elements: A Spectral Approach,
Springer-Verlag,
New York.

Ghanem,
R.
,
Red-Horse,
J.
, and
Sarkar,
A.
, 2000, “
Modal Properties of a Space-Frame With Localized System Uncertainties,” PMC2000, ASCE Probabilistic Mechanics Conference, Notre Dame, IN, June 24–26.

Xiu,
D.
,
Lucor,
D.
,
Su,
C.-H.
, and
Karniadakis,
G. E.
, 2002, “
Stochastic Modeling of Flow–Structure Interactions Using Generalized Polynomial Chaos,” ASME J. Fluids Eng.,
124(1), pp. 51–59.

[CrossRef]
Ghanem,
R.
, 1999, “
Stochastic Finite Elements for Heterogeneous Media With Multiple Random Non-Gaussian Properties,” J. Eng. Mech. (ASCE),
125(1), pp. 26–40.

[CrossRef]
Kim,
D.
,
Debusschere,
B. J.
, and
Najm,
H. N.
, 2007, “
Spectral Methods for Parametric Sensitivity in Stochastic Dynamical Systems,” Biophys. J.,
92(2), pp. 379–393.

[CrossRef] [PubMed]
Fagiano,
L.
, and
Khammash,
M.
, 2012, “
Simulation of Stochastic Systems Via Polynomial Chaos Expansions and Convex Optimization,” Phys. Rev. E,
86(3), p. 036702.

[CrossRef]
Hover,
F. S.
, and
Triantafyllou,
M. S.
, 2006, “
Application of Polynomial Chaos in Stability and Control,” Automatica,
42(5), pp. 789–795.

[CrossRef]
Eldred,
M. S.
, and
Burkhardt,
J.
, 2009, “
Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification,” AIAA Paper No. 2009-976.

Mukherjee,
R.
, and
Anderson,
K. S.
, 2007, “
An Orthogonal Complement Based Divide-and-Conquer Algorithm for Constrained Multibody Systems,” Nonlinear Dyn.,
48(1–2), pp. 199–215.

[CrossRef]
Poursina,
M.
, and
Anderson,
K.
, 2013, “
An Extended Divide-and-Conquer Algorithm for a Generalized Class of Multibody Constraints,” Multibody Syst. Dyn.,
29(3), pp. 235–254.

[CrossRef]
Xiu,
D.
, and
Karniadakis,
G. E.
, 2002, “
The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations,” SIAM J. Sci. Comput.,
24(2), pp. 619–644.

[CrossRef]
Cameron,
R. H.
, and
Martin,
W. T.
, 1947, “
The Orthogonal Development of Non-Linear Functionals in Series of Fourier–Hermite Functionals,” Ann. Math.,
48(2), pp. 385–392.

[CrossRef]
Featherstone,
R.
, 1999, “
A Divide-and-Conquer Articulated Body Algorithm for Parallel

*O*(log(

*n*)) Calculation of Rigid Body Dynamics. Part 1: Basic Algorithm,” Int. J. Rob. Res.,
18(9), pp. 867–875.

[CrossRef]
Featherstone,
R.
, 1999, “
A Divide-and-Conquer Articulated Body Algorithm for Parallel

*O*(log(

*n*)) Calculation of Rigid Body Dynamics. Part 2: Trees, Loops, and Accuracy,” Int. J. Rob. Res.,
18(9), pp. 876–892.

[CrossRef]
Laflin,
J.
,
Anderson,
K. S.
,
Khan,
I. M.
, and
Poursina,
M.
, 2014, “
Advances in the Application of the Divide-and-Conquer Algorithm to Multibody System Dynamics,” ASME J. Comput. Nonlinear Dyn.,
9(4), p. 041003.

[CrossRef]
Laflin,
J.
,
Anderson,
K. S.
,
Khan,
I. M.
, and
Poursina,
M.
, 2014, “
New and Extended Applications of the Divide-and-Conquer Algorithm for Multibody Dynamics,” ASME J. Comput. Nonlinear Dyn.,
9(4), p. 041004.

[CrossRef]
Poursina,
M.
,
Khan,
I.
, and
Anderson,
K. S.
, 2012, “
Efficient Model Transition in Adaptive Multi-Resolution Modeling of Biopolymers,” Linear Algebra Theorems and Applications,
H. A. Yasser
, ed.
INTECH, Croatia, pp. 237–250.

Bhalerao,
K. D.
,
Poursina,
M.
, and
Anderson,
K. S.
, 2010, “
An Efficient Direct Differentiation Approach for Sensitivity Analysis of Flexible Multibody Systems,” Multibody Syst. Dyn.,
23(2), pp. 121–140.

[CrossRef]
Mukherjee,
R.
, and
Anderson,
K. S.
, 2007, “
A Logarithmic Complexity Divide-and-Conquer Algorithm for Multi-Flexible Articulated Body Systems,” Comput. Nonlinear Dyn.,
2(1), pp. 10–21.

[CrossRef]
Mukherjee,
R. M.
, and
Anderson,
K. S.
, 2007, “
Efficient Methodology for Multibody Simulations With Discontinuous Changes in System Definition,” Multibody Syst. Dyn.,
18(2), pp. 145–168.

[CrossRef]
Mukherjee,
R. M.
,
Bhalerao,
K. D.
, and
Anderson,
K. S.
, 2007, “
A Divide-and-Conquer Direct Differentiation Approach for Multibody System Sensitivity Analysis,” Struct. Multidiscip. Optim.,
35(5), pp. 413–429.

[CrossRef]
Poursina,
M.
, and
Anderson,
K. S.
, 2013, “
Canonical Ensemble Simulation of Biopolymers Using a Coarse-Grained Articulated Generalized Divide-and-Conquer Scheme,” Comput. Phys. Commun.,
184(3), pp. 652–660.

[CrossRef]
Malczyk,
P.
, and
Frczek,
J.
, 2014, “
Molecular Dynamics Simulation of Simple Polymer Chain Formation Using Divide and Conquer Algorithm Based on the Augmented Lagrangian Method,” Proc. Inst. Mech. Eng., Part K,
229(2), pp. 116–131.

Roberson,
R. E.
, and
Schwertassek,
R.
, 1988, Dynamics of Multibody Systems,
Springer-Verlag, Berlin.