Traveling along a zipline
نویسندگان
چکیده
The trajectory of a rider slowly traversing a zipline of fixed length and endpoints is computed, as a one-dimensional illustration of the curving of spacetime by a mass. As the rider’s weight increases from 0 to ∞, the trajectories uniformly interpolate between a catenary and an ellipse. These results are obtained by balancing forces in the horizontal and vertical directions, so that the treatment is accessible to undergraduate physics majors who have been exposed to finding the numerical roots of an algebraic equation.
منابع مشابه
Traveling Vortex Helices for Schrödinger Map Equations
We construct traveling wave solutions with vortex helix structures for the Schrödinger map equation ∂m ∂t = m× (∆m−m3~e3) on R × R, of the form m(s1, s2, s3 − δ| log | t) with traveling velocity δ| log | along the direction of s3 axis. We use a perturbation approach which gives a complete characterization of the asymptotic behavior of the solutions.
متن کاملTraveling Vortex Helicies for Schrödinger Map Equation
We construct traveling wave solutions with vortex helices for the Schrödinger map equation ∂m ∂t = m× (∆m−m3~e3) in R × R, of the form m(s1, s2, s3 − δ| log | t) with traveling velocity δ| log | along the direction of s3 axis. We use a perturbation approach which gives a complete characterization of the asymptotic behavior of the solutions.
متن کاملThe Stop Location Problem with Realistic Traveling Time
In this paper we consider the location of stops along the edges of an already existing public transportation network. This can be the introduction of bus stops along some given bus routes, or of railway stations along the tracks in a railway network. The positive effect of new stops is given by the better access of the customers to the public transport network, while the traveling time increase...
متن کاملar X iv : g r - qc / 9 20 90 02 v 2 3 1 O ct 1 99 2 Black string traveling waves
A family of solutions to low energy string theory is found. These solutions represent waves traveling along “extremal black strings.” 2
متن کاملNew Heuristic Algorithms for Solving Single-Vehicle and Multi-Vehicle Generalized Traveling Salesman Problems (GTSP)
Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP)expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...
متن کامل