In this paper, we study a numerical method for the computation and continuation of homoclinic and heteroclinic orbits based upon the arclength parameterization of the orbits. Unlike most other methods, this method utilizes the geometric structure of the homoclinic and heteroclinic orbits and does not require solving a boundary value problem on an innnite interval. However, the boundary value pr...

Deep water waves in two-dimensional flow can have curvature singularities on the surface profile, for example, the limiting Stokes wave has a corner of 2π/3 radians and the limiting standing wave momentarily forms a corner of π/2 radians. Much less is known about the possible formation of curvature singularities in general. A novel way of exploring this possibility is to consider the curvature ...

The power system nonlinearity and its profound impact on the individual states of power system is first evaluated and the interaction between their constituent modes during the occurrence of internal mode resonance (IMR) is discussed in this paper. A typical dynamical feature of nonlinear systems is the frequency-energy dependence of their states and their corresponding constituent modes which ...

Modeling, control, and stabilization of dynamics of two-dimensional object grasping by using a pair of multijoint robot fingers are investigated under rolling contact constraints and an arbitrary geometry of the object and fingertips. First, a fundamental testbed problem of modeling and control of rolling motion between 2-D rigid bodies with an arbitrary shape is treated under the assumption th...

We study the mechanical property of a two-dimensional filament with constant spontaneous curvature and under uniaxial applied force. We derive the equation that governs the stable shape of the filament and obtain analytical solutions for the equation. We find that for a long filament with positive initial azimuth angle (the azimuth angle is the angle between x axis and the tangent of the filame...

Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine-invariant arclength for surfaces in R in order to extend the set of existing non-rigid shape analysis tools. We show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated...

Motivated by the inadequacy of conducting atomistic simulations crack propagation using static boundary conditions that do not reflect movement tip, we extend Sinclair's flexible condition algorithm [J. E. Sinclair, Philos. Mag. 31, 647 (1975)] and propose a numerical-continuation-enhanced scheme, enabling full solution paths for cracks to be computed with pseudo-arclength continuation, present...