# Why can a free-falling cat always manage to land safely on its feet?

@article{Zhen2015WhyCA, title={Why can a free-falling cat always manage to land safely on its feet?}, author={Shengchao Zhen and Kang Huang and H. Zhao and Ye‐Hwa Chen}, journal={Nonlinear Dynamics}, year={2015}, volume={79}, pages={2237-2250} }

Udwadia–Kalaba equation is a simple, aesthetic and thought-provoking description of the world at a very fundamental level. It is about the way systems of bodies move. We creatively apply the Udwadia–Kalaba approach to study falling cat’s movements. The cat is modeled as a constrained discrete dynamical system. In an alternative way, Udwadia–Kalaba formulation is used for analysis of the falling cat’s dynamics. With this novel approach, we can easily obtain the dynamical model and get the… Expand

#### 14 Citations

Modern explorations of the Brachistochrone-related problem: using the Udwadia–Kalaba approach

- Mathematics
- Mathematics and Mechanics of Solids
- 2018

Modern explorations regarding the search for a curve subject to a minimization principle and its inverse, namely the search for the minimization object based on a given curve, are made. By using the… Expand

Effect of swing legs on turning motion of a free-falling cat robot

- Engineering
- ICMA 2017
- 2017

Based on self-righting principle of a free-falling cat, a multi-rigid-body dynamic model of a cat robot is built with the consideration of swing legs and the relation between turning rate and swing… Expand

Effect of swing legs on turning motion of a free-falling cat robot

- 2017 IEEE International Conference on Mechatronics and Automation (ICMA)
- 2017

Based on self-righting principle of a free-falling cat, a multi-rigid-body dynamic model of a cat robot is built with the consideration of swing legs and the relation between turning rate and swing… Expand

Application of the Udwadia–Kalaba approach to tracking control of mobile robots

- Mathematics
- 2016

Udwadia–Kalaba approach which presents a new, general and explicit equation of motion for constrained mechanical systems with holonomic or nonholonomic constraints is applied to the trajectory… Expand

Dynamic modeling of dual-arm cooperating manipulators based on Udwadia–Kalaba equation

- Mathematics
- 2016

Dual-arm cooperating manipulators subject to a certain constraint brought about by the desired trajectory and geometric constraint show high nonlinearity and coupling in their dynamic characteristic.… Expand

Concise method to the dynamic modeling of climbing robot

- Engineering
- 2017

With the aim of dynamic modeling of the climbing robot with dual-cavity structure and wheeled locomotion mechanism, a succinct and explicit equation of motion based on the Udwadia–Kalaba equation is… Expand

A hierarchical constraint approach for dynamic modeling and trajectory tracking control of a mobile robot

- Computer Science
- 2021

A creative hierarchical constraint approach based on the Udwadia–Kalaba theory is proposed and the asymptotic convergence criterion is proposed to deal with the dynamic model and trajectory tracking control force of the wheeled mobile robot at the same time. Expand

Simple method to the dynamic modeling of industrial robot subject to constraint

- Computer Science
- 2016

The modified algorithm proposed can be more precisely utilized in dynamics modeling of industrial robot subject to constraint by reducing the errors obtained by integrating the constrained dynamic equation. Expand

Trajectory tracking control of two degrees-of-freedom helicopter based on Udwadia–Kalaba theory

- Computer Science
- Advances in Mechanical Engineering
- 2018

Simulation results show that the modified controller can drive the 2-degrees-of-freedom helicopter to perfectly track the desired trajectory with less control cost and high control accuracy. Expand

Constraint-Following Control for Mobile Robots: A Hierarchical Approach

- Computer Science
- 2019 1st International Conference on Industrial Artificial Intelligence (IAI)
- 2019

This study addresses the problem of constraint-following control of mobile robots with different categories of constraints by using a hierarchical approach based on Udwadia-Kalaba theory. Expand

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