The ankle joint of currently available powered prostheses is capable of controlling one degree of freedom (DOF), focusing on improved mobility in the sagittal plane. To increase agility, the requirements of turning in prosthesis design need to be considered. Ankle kinematics and kinetics were studied during sidestep cutting and straight walking. There were no significant differences between the...

and not concrete entities. I shall call it physical dependence. The correlative, and more basic, notion is that of physical independence: it is in fact the notion of degree offreedom. The idea is this: X is a physically independent quantity whenever it is among those quantities whose magnitudes shape the state of a system to which they belong, and it is physically dependent when it is given sha...

We define and study kinematical observables involving fermion spin, such as the total spin of a collection particles, in loop quantum gravity. Due to requirement gauge invariance, relevant states contain strong entanglement between gravity fermionic degrees freedom. Interestingly we find that properties spectra are nevertheless similar their counterparts from mechanics. However, there also new ...

Motivated by recent studies of superconformal mechanics extended spin degrees freedom, we construct minimally superintegrable models spinning particles on 2-sphere, the freedom which are represented a 3-vector obeying structure relations 3d real Lie algebra. Generalisations involving an external field Dirac monopole, or motion group manifold SU(2), scalar potential giving rise to two quadratic ...

We study the classical and quantum dynamics of generally covariant theories with vanishing Hamiltonian and with a finite number of degrees of freedom. In particular, the geometric meaning of the full solution of the relational evolution of the degrees of freedom is displayed, which means the determination of the total number of evolving constants of motion required. Also a method to find evolvi...

We derive estimates on the upper bounds of the asymptotic degrees of freedom for strong solutions of the two-dimensional Navier–Stokes equations with no-slip and nonhomogeneous boundary conditions. The analysis is also extended to an abstract equation modelling some other equations in fluid mechanics. Similar results are obtained. AMS classification scheme numbers: 35Q30, 37L30, 76D05

We present an analytic example of two dimensional quantum mechanical system, where the exponential suppression of the probability of over–barrier reflection changes non-monotonically with energy. The suppression is minimal at certain “optimal” energies where reflection occurs with exponentially larger probability than at other energies.