## 2 Citations

### A Self-Stabilized Inverted Pendulum Made of Optically Responsive Liquid Crystal Elastomers

- PhysicsFrontiers in Robotics and AI
- 2021

The inverted pendulum system has great potential for various engineering applications, and its stabilization is challenging because of its unstable characteristic. The well-known Kapitza’s pendulum…

### Stability and pre-thermalization in chains of classical kicked rotors

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2018

Periodic drives are a common tool to control physical systems, but have a limited applicability because time-dependent drives generically lead to heating. How to prevent the heating is a fundamental…

## References

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- PhysicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2001

Results on the dynamics of the planar pendulum with parametric vertical timeperiodic forcing are reviewed and extended. Numerical methods are employed to study the various dynamical features of the…

### On the dynamic stabilization of an inverted pendulum

- Physics
- 2001

A simple qualitative physical explanation is suggested for the phenomenon of dynamic stabilization of the inverted rigid planar pendulum whose pivot is constrained to oscillate with a high frequency…

### Kam theory, Lindstedt series and the stability of the upside-down pendulum

- Physics
- 2002

We
consider the planar pendulum with support point oscillating in the
vertical direction; the upside-down position of the pendulum
corresponds to an equilibrium point for the projection of the …

### Stability and Hopf bifurcations in an inverted pendulum

- Physics, Mathematics
- 1992

The inverted state of a simple pendulum is a configuration of unstable equilibrium. This instability may be removed if the pivot is harmonically displaced up and down with appropriate frequency and…

### On the synchronization of chains of nonlinear pendula connected by linear springs

- Physics
- 2014

In this work the theoretical model of multidimensional physical systems, representable as chains of nonlinearly coupled chaotic pendula subjected to harmonic excitations, is formulated and its…

### On the stability of the upside–down pendulum with damping

- PhysicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2001

A rigorous analysis is presented in order to show that, in the presence of friction, the upward equilibrium position of the vertically driven pendulum, with a small nonvanishing damping term, becomes…

### The inverted pendulum : A singularity theory approach

- Mathematics
- 1999

The inverted pendulum with small parametric forcing is considered as an example of a wider class of parametrically forced Hamiltonian systems. The qualitative dynamics of the Poincare map…

### Nonlinear behavior and control of a nonholonomic free-joint manipulator

- EngineeringIEEE Trans. Robotics Autom.
- 1997

This work analyzes the nonlinear behavior of a two-joint planar manipulator with the second joint free from nonlinear dynamics point of view and proposes an amplitude modulation of the feedback error.

### Bifurcations and transitions to chaos in an inverted pendulum

- Mathematics, Physics
- 1998

We consider a parametrically forced pendulum with a vertically oscillating suspension point. It is well known that, as the amplitude of the vertical oscillation is increased, its inverted state…