This paper investigates dynamics of double pendulum subjected to vertical parametric kinematic excitation. It includes detailed bifurcation diagrams in two parameters space (excitation's frequency and amplitude) for both oscillations and rotations in the domain of periodic solutions.

In this paper the swing-up problem for the Furuta pendulum is solved applying Fradkov’s speed-gradient (SG) method [1, 9] to a dimension 4 model of the system. The new law is compared with the conventional Åström-Furuta strategy, based on a dimension 2 model. A comparative analysis, including simulations and experiments, whereby the advantages and effectiveness of the new law for swinging the p...

The physics of swinging a tennis racquet is examined by modeling the forearm and the racquet as a double pendulum. We consider differences between a forehand and a serve, and show how they differ from the swing of a bat and a golf club. It is also shown that the swing speed of a racquet, like that of a bat or a club, depends primarily on its moment of inertia rather than on its mass. © 2011 Ame...

The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating galaxy is considered as the the giant galactical gyroscope. The Lorentz equation and the Bargmann-MichelTelegdi equations are generalized for the rotati...

It is well-known that a suitably designed unpowered mechanical biped robot can \walk" down an inclined plane with a steady gait. The characteristics of the gait (e.g., velocity, time period, step length) depend on the geometry and the inertial properties of the robot and the slope of the plane. A passive motion has the distinction of being \natu-ral" and is likely to enjoy energy optimality. In...

The Standard Model Extension (SME) provides the most general observer-independent field theoretical framework for investigations of Lorentz violation. The SME lagrangian by definition contains all Lorentz-violating interaction terms that can be written as observer scalars and that involve particle fields in the Standard Model and gravitational fields in a generalized theory of gravity. This inc...

In this paper we develop a robust controller based on variable structure systems (VSS) control theory for the stabilization of a class of Underactuated Mechanical Systems. This controller is based on a noncollocated partial feedback linearization of the underactuated system with a particular choice of the additional control for which the design is made using the sliding mode approach. Simulatio...

In initial value problems for ODEs with interval-valued parameters, it is desirable in many applications to be able to determine a validated enclosure of all possible solutions to the ODE system. Much work has been done for the case in which initial values are given by intervals, and there are several available software packages that deal with this case. However, relatively little work has been...

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of analytic integrals. We also consider the potential systems on adjoint orbits, wh...

An overview of the application of physics to the game of golf is given. The golf swing is modelled as a double pendulum. This model and its variations have been used extensively by researchers in determining the effect that various swing parameters have on clubhead speed. These results as well as examples of three-link models are discussed. Kinematic and kinetic measurements taken on the record...