This paper addresses the problem of designing jerk limited timeoptimal control profiles for rest-to-rest maneuvers of flexible structures. The variation of the structure of the jerk profile as a function of the permissible jerk is studied. An optimal control problem is formulated which includes constraints to cancel the poles corresponding to the rigid body and flexible modes of the system and ...

We investigate the dynamics of a system involving the planar motion of a rigid body which is restrained by linear springs and which possesses a skate-like nonholonomic constraint known as C̆aplygin’s sleigh. It is shown that the system can be reduced to one with 2 2 degrees of freedom. The resulting phase flow is shown to involve a curve of nonisolated equilibria. Using second-order averaging, t...

The problem of designing jerk limited-time optimal control proŽ les for rest-to-rest maneuvers of  exible structures with multiple actuators is addressed. The problem formulation includes constraints to cancel the poles corresponding to the rigid-body mode and  exible modes of the system and to satisfy the boundary conditions of the rest-to-rest maneuver. Further constraints can be added to i...

We subjected the time series of quasi-rigid-body vibration pulses (elastic emissions) from laboratory fracture carried out by a piezoelectric accelerometer on concrete and rock specimens under uniaxial compression to statistical analysis. In both cases, we find that the waiting-time distribution can be described by a scaling law extending over several orders of magnitude. This law is indistingu...

This paper gives necessary and sufficient conditions for the (n-dimensional) generalized free rigid body to be in a state of relative equilibrium. The conditions generalize those for the case of the three-dimensional free rigid body, namely that the body is in relative equilibrium if and only if its angular velocity and angular momentum align, that is, if the body rotates about one of its princ...

Structural and molecular changes in 1,1-diamino-2,2-dinitroethylene (DADNE, FOX-7) compressed to high pressures were investigated using both anvil cell experiments and ab-initio calculations. The experiments consisted of angledispersive x-ray diffraction analysis and Raman spectroscopy with compression. The results indicated higher compression along the b-axis than along the aor caxis, and a tr...

‎the water wave generation by wave paddle and a freely falling rigid body are examined by using an incompressible smoothed particle hydrodynamics (isph)‎. ‎in the current isph method‎, ‎the pressure was evaluated by solving pressure poisson equation using a semi-implicit algorithm based on the projection scheme and the source term of pressure poisson equation contains both of divergence free ve...

Glasses have a large excess of low-frequency vibrational modes in comparison with continuous elastic body, the so-called Boson Peak, which appears to correlate with several crucial properties of glasses, such as transport or fragility. I review recent results showing that the Boson Peak is a necessary consequence of the weak connectivity of the solid. I explain why in assemblies repulsive spher...

This series of four papers comprises a theoretical investigation into twisting somersaults. Both simple and complex mathematical models are used to provide an understanding of the mechanics of the production and removal of twist in somersaults. Various twisting techniques are evaluated and a method is developed for the partitioning of an actual performance into contributions from these twisting...

It has been usual in most old-style text books for dynamics to treat the formulas describing linear(or translational) and angular(or rotational) motion of a rigid body separately. For example, the famous Newton’s 2nd law, f = ma, for the translational motion of a rigid body has its partner, so-called the Euler’s equation which describes the rotational motion of the body. Separating translation ...