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Keywords
(7)
Complex Dynamics
Degree of Freedom
Invariant Manifold
Nonlinear Dynamics
Relative Equilibria
Rigid Body
Center of Mass
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Nonlinear Dynamics of the 3D Pendulum
Nonlinear Dynamics of the 3D Pendulum,10.1007/s0033201090786,Journal of Nonlinear Science,NALIN A. CHATURVEDIy,Taeyoung Lee,Melvin Leok,N. Harris M
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Nonlinear Dynamics of the 3D Pendulum
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Citations: 3
)
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NALIN A. CHATURVEDIy
,
Taeyoung Lee
,
Melvin Leok
,
N. Harris McClamroch
A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the
rigid body
is asymmetric and the
center of mass
is distinct from the pivot location leads to the 3D pendulum. Full and reduced 3D pendulum models are introduced and used to study important features of the nonlinear dynamics: conserved quantities, equilibria, invariant manifolds, local dynamics near equilibria and invariant manifolds, and the presence of chaotic motions. These results demonstrate the rich and
complex dynamics
of the 3D pendulum.
Journal:
Journal of Nonlinear Science  J NONLINEAR SCI
, vol. 21, no. 1, pp. 332, 2011
DOI:
10.1007/s0033201090786
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Citation Context
(3)
...These topological issues arise in other applications involving rotational degrees of freedom, like pendulum systems [
11
], robotic manipulators [12], and gimbalpointing mechanisms (e.g., a pantilt camera) [13], among others (see [4, Table 1] for several examples)...
Christopher G. Mayhew
,
et al.
QuaternionBased Hybrid Control for Robust Global Attitude Tracking
...about the vertical axis, which allows the configuration space to be reduced to the quotient space SO(3)/S1 ≃ S2 [
9
]...
...As described in [
9
], the global dynamics of the 3D pendulum are complicated...
Taeyoung Lee
,
et al.
Propagation of uncertainty in rigid body attitude flows
...The attitude dynamics of a rigid body may be chaotic [
24
]...
Taeyoung Lee
.
Computational Geometric Mechanics, Control, and Estimation of Rigid Bo...
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Sort by:
Citations
(3)
QuaternionBased Hybrid Control for Robust Global Attitude Tracking
(
Citations: 4
)
Christopher G. Mayhew
,
Ricardo G. Sanfelice
,
Andrew R. Teel
Journal:
IEEE Transactions on Automatic Control  IEEE TRANS AUTOMAT CONTR
, vol. 56, no. 11, pp. 25552566, 2011
Propagation of uncertainty in rigid body attitude flows
(
Citations: 5
)
Taeyoung Lee
,
Nalin A. Chaturvedi
,
Amit K. Sanyal
,
Melvin Leok
,
N. Harris McClamroch
Conference:
Conference on Decision and Control  CDC
, pp. 26892694, 2007
Computational Geometric Mechanics, Control, and Estimation of Rigid Bodies
Taeyoung Lee