Jet Methods in Time-Dependent Lagrangian Biomechanics

In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration manifold, called the configuration bundle. We start with an ordinary configuration manifold of human body motion, given as a set of its all active degrees of freedom (DOF) for a particular movement. This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. By this extension, using techniques from fibre bundles, we defined the biomechanical configuration bundle. On the biomechanical bundle we define vector-fields, differential forms and affine connections, as well as the associated jet manifolds. Using the formalism of jet manifolds of velocities and accelerations, we develop the time-dependent Lagrangian biomechanics. Its underlying geometric evolution is given by the Ricci flow equation. Keywords: Human time-dependent biomechanics, configuration bundle, jet spaces, Ricci flowComment: 13 pages, 3 figure

Near-lunar proton velocity distribution explained by electrostatic acceleration

The observation of parallel ion velocity in the near-lunar wake approximately equal to external solar wind velocity \emph{can} be explained within uncertainties by an analytic electrostatic expansion model. The one-dimensional model frequently used is inadequate because it does not account for the moon's spherical shape. However, application of a more recent generalization to three-dimensions of the solution along characteristics predicts higher velocities, and is probably sufficient to account for the SARA observations on the Chandrayaan-1 space-craft.Comment: 1 figure, 1 tabl

Gravity stabilized flying vehicle Patent

Hovering type flying vehicle design and principle mechanisms for manned or unmanned us