Marsden,
J. E.
, and
Ratiu,
T. S.
, 1999, Introduction to Mechanics and Symmetry,
Springer-Verlag,
New York.

Bloch,
A. M.
,
Krishnaprasad,
P. S.
,
Marsden,
J. E.
, and
Murray,
R. M.
, 1996, “
Nonholonomic Mechanical Systems With Symmetry,” Arch. Ration. Mech. Anal.,
136(1), pp. 21–99.

[CrossRef]
Bloch,
A. M.
, 2003, Nonholonomic Mechanics and Control,
Springer, New York.

Koon,
W. S.
, and
Marsden,
J. E.
, 1997, “
The Hamiltonian and Lagrangian Approaches to the Dynamics of Nonholonomic Systems,” Rep. Math. Phys.,
40(1), pp. 21–62.

[CrossRef]
Chhabra,
R.
, and
Emami,
M. R.
, 2016, “
A Unified Approach to Input-Output Linearization and Concurrent Control of Underactuated Open-Chain Multi-Body Systems With Holonomic and Nonholonomic Constraints,” J. Dyn. Control Syst.,
22(1), pp. 129–168.

[CrossRef]
Chhabra,
R.
, 2016, “
Dynamical Reduction and Output-Tracking Control of the Lunar Exploration Light Rover (LELR),” 2016 IEEE, Aerospace Conference, Mar. 5–12, Big Sky, MT.

Bullo,
F.
, and
Zefran,
M.
, 2002, “
On Mechanical Control Systems With Nonholonomic Constraints and Symmetries,” Syst. Control Lett.,
45(2), pp. 133–143.

[CrossRef]
Olfati-Saber,
R.
, 2001, “
Nonlinear Control of Underactuated Mechanical Systems With Application to Robotics and Aerospace Vehicles,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.

Ferrario,
C.
, and
Passerini,
A.
, 2000, “
Rolling Rigid Bodies and Forces of Constraint: An Application to Affine Nonholonomic Systems,” Meccanica,
35(5), pp. 433–442.

[CrossRef]
Sun,
W.
,
Wu,
Y. Q.
, and
Sun,
Z. Y.
, 2014, “
Tracking Control Design for Nonholonomic Mechanical Systems With Affine Constraints,” Int. J. Autom. Comput.,
11(3), pp. 328–333.

[CrossRef]
Fassó,
F.
, and
Sansonetto,
N.
, 2015, “
Conservation of Energy and Momenta in Nonholonomic Systems With Affine Constraints,” Regular Chaotic Dyn.,
20(4), pp. 449–462.

[CrossRef]
Noether,
E.
, 1918, “
Invariante Variationsprobleme, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen,” Mathematisch-Physikalische Klasse, pp. 235–257.

Marsden,
J. E.
, and
Weinstein,
A.
, 1974. “
Reduction of Symplectic Manifolds With Symmetry,” Rep. Math. Phys.,
5(1), pp. 121–130.

[CrossRef]
Routh,
E. J.
, 1882, A Treatise on the Dynamics of a System of Rigid Bodies. With Numerous Examples: The Elementary Part,
Macmillan, London.

Marsden,
J. E.
, 1992, Lectures on Mechanics,
Cambridge University Press, New York.

Planas-Bielsa,
V.
, 2004, “
Point Reduction in Almost Symplectic Manifolds,” Rep. Math. Phys.,
54(3), pp. 295–308.

[CrossRef]
Marsden,
J. E.
,
Misiolek,
G.
, and
Ortega,
J. P.
, 2007, Hamiltonian Reduction by Stages, 1st ed.,
Springer-Verlag,
Berlin.

Chhabra,
R.
, and
Emami,
M. R.
, 2015, “
Symplectic Reduction of Holonomic Open-Chain Multi-Body Systems With Constant Momentum,” J. Geom. Phys.,
89, pp. 82–110.

[CrossRef]
Koon,
W. S.
, and
Marsden,
J. E.
, 1998, “
Poisson Reduction for Nonholonomic Mechanical Systems With Symmetry,” Rep. Math. Phys.,
42(1–2), pp. 101–134.

[CrossRef]
Cendra,
H.
,
Marsden,
J. E.
, and
Ratiu,
T. S.
, 2001, Lagrangian Reduction by Stages, Vol.
722,
American Mathematical Society, Providence, RI.

Marsden,
J. E.
, and
Scheurle,
J.
, 1993, “
The Reduced Euler–Lagrange Equations,” Fields Inst. Commun.,
1, pp. 139–164.

Marsden,
J. E.
, and
Scheurle,
J.
, 1993, “
Lagrangian Reduction and the Double Spherical Pendulum,” Z. Angew. Math. Phys.,
44(1), pp. 17–43.

[CrossRef]
Chaplygin,
S.
, 2008, “
On the Theory of Motion of Nonholonomic Systems. The Reducing-Multiplier Theorem,” Regular Chaotic Dyn.,
13(4), pp. 369–376 [Matematicheskiĭ sbornik, 28(1) (1911)].

[CrossRef]
Koiller,
J.
, 1992, “
Reduction of Some Classical Non-Holonomic Systems With Symmetry,” Arch. Ration. Mech. Anal.,
118(2), pp. 113–148.

[CrossRef]
van der Schaft,
A. J.
, and
Maschke,
B. M.
, 1994, “
On the Hamiltonian Formulation of Nonholonomic Mechanical Systems,” Rep. Math. Phys.,
34(2), pp. 225–233.

[CrossRef]
Yoshimura,
H.
, and
Marsden,
J. E.
, 2006, “
Dirac Structures in Lagrangian Mechanics Part II: Variational Structures,” J. Geom. Phys.,
57(1), pp. 209–250.

[CrossRef]
Cendra,
H.
,
Marsden,
J. E.
, and
Ratiu,
T. S.
, 2001, “
Geometric Mechanics, Lagrangian Reduction and Nonholonomic Systems,” Mathematics Unlimited-2001 and Beyond,
Springer-Verlag, Berlin, pp. 221–273.

Chhabra,
R.
, and
Emami,
M. R.
, 2014, “
Nonholonomic Dynamical Reduction of Open-Chain Multi-Body Systems: A Geometric Approach,” Mech. Mach. Theory,
82, pp. 231–255.

[CrossRef]
Ohsawa,
T.
,
Fernandez,
O. E.
,
Bloch,
A. M.
, and
Zenkov,
D. V.
, 2011, “
Nonholonomic Hamilton-Jacobi Theory Via Chaplygin Hamiltonization,” J. Geom. Phys.,
61(8), pp. 1263–1291.

[CrossRef]
Hochgerner,
S.
, and
Garcia-Naranjo,
L.
, 2009, “
G-Chaplygin Systems With Internal Symmetries, Truncation, and an (Almost) Symplectic View of Chaplygin's Ball,” J. Geom. Mech.,
1(1), pp. 35–53.

[CrossRef]
Bates,
L.
, and
Śniatycki,
J.
, 1993, “
Nonholonomic Reduction,” Rep. Math. Phys.,
32(1), pp. 99–115.

[CrossRef]
Cushman,
R.
,
Kemppainen,
D.
,
Śniatycki,
J.
, and
Bates,
L.
, 1995, “
Geometry of Nonholonomic Constraints,” Rep. Math. Phys.,
36(2/3), pp. 275–286.

[CrossRef]
Cushman,
R.
, and
Śniatycki,
J.
, 2002, “
Nonholonomic Reduction for Free and Proper Actions,” Reg. Chaotic Dyn.,
7(1), pp. 61–72.

[CrossRef]
Cushman,
R.
,
Duistermaat,
H.
, and
Śniatycki,
J.
, 2009, Geometry of Nonholonomically Constrained Systems,
World Scientific Publishing Company, Singapore.

Śniatycki,
J.
, 1998, “
Nonholonomic Noether Theorem and Reduction of Symmetries,” Rep. Math. Phys.,
42(1/2), pp. 5–23.

[CrossRef]
Śniatycki,
J.
, 2001, “
Almost Poisson Spaces and Nonholonomic Singular Reduction,” Rep. Math. Phys.,
48(1/2), pp. 235–248.

[CrossRef]
Gay-Balmaz,
F.
, and
Yoshimura,
H.
, 2015, “
Dirac Reduction for Nonholonomic Mechanical Systems and Semidirect Products,” Adv. Appl. Math.,
63, pp. 131–213.

[CrossRef]