This paper presents a general quadratic optimization methodology for autonomous path planning of spatial rigid motion with constrained attitude. The motion to be planned has six degrees of freedom and is assumed under constant velocity in the body frame. The objective is to determine the motion orientation (or attitude), handled as control variables, along the planned paths. A procedure is disc...

This paper presents optimal dimensional synthesis of a planar, single degree of freedom, sixbar Stephenson mechanism having rotational constraints. The prescribed parameters of the mechanism are displacement vector and coupler link motion. The aim of the present work is to determine the optimized dimensions and orientation of various links of the mechanism that is capable to follow the prescrib...

Four experiments demonstrate that lines indicating path of movement can generate rotational percepts in a multistable motion display that usually produces only horizontal or vertical motion percepts. The properties of the path-of-movement lines are predicted by a neural-network theory of visual perception. Experimental results validate the theory's predictions by demonstrating that movement of ...

Using path integral Monte Carlo simulations we calculate exchange frequencies in bulk hcp 4He as atoms undergo ring exchange. We fit the frequencies to a lattice model and examine whether such atoms could become a supersolid, that is, have a nonclassical rotational inertia. We find that the scaling with respect to the number of exchanging atoms is such that superfluid behavior will not be obser...

The exact path integration for a family of maximally super-integrable systems generalizing the hydrogen atom in the n-dimensional Euclidean space is presented. The Green’s function is calculated in parabolic rotational and spherical coordinate systems. The energy spectrum and the correctly normalized wave functions of the bound states are obtained from the poles of the Green’s function and thei...

We study the Laplacian-∞ path as an extreme case of the Laplacian-α random walk. Although, in the finite α case, there is reason to believe that the process converges to SLEκ, with κ = 6/(2α+ 1), we show that this is not the case when α = ∞. In fact, the scaling limit depends heavily on the lattice structure, and is not conformal (or even rotational) invariant.

Abstract This paper describes an attempt to address some of the deficiencies and infelicities associated with the use of piecewise Bézier segments when constructing a smooth path for a camera in a computer animation. In particular, techniques are presented for rotational interpolation, ensuring continuity where the time intervals between key-frames are variable and generating curve segments wit...

For n even, a factorization of a complete graph Kn is a partition of the edges into n−1 perfect matchings, called the factors of the factorization. With respect to a factorization, a path is called rainbow if its edges are from distinct factors. A rainbow Hamiltonian path takes exactly one edge from each factor and is called orthogonal to the factorization. It is known that not all factorizatio...

The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direc...

In both classical and quantum mechanics, a dynamical system with symmetry is reduced to a system which has a smaller number of degrees of freedom. In this paper we formulate path integrals for the quantum system reduced by symmetry. The original system is defined in terms of a Riemannian manifold M , on which a Lie group G acts by isometric transformations. Then we show that the path integral o...