Programming an Analog Computer for a Large Class of Trajectories
Abstract
The negative gradient method is extended to the stable analog computer programming of a class of time varying trajectory problems defined by phi (x, t) 0, f(x,u,t) 0, u x where x and u are n-dimensional vectors,s an m-dimensional position vector function (m < n), and f is an (n - m) dimensional velocity vector function. This class of problems includes the amplitude stabilized oscillator, two-dimensional contour tracing, conic section generation and three-dimensional trajectory plotting when at least the first integral of the equations of motion are available. An augmented velocity vector function is defined which provides n independent equations f' 0. For a fixed x, these equations can be solved for u in the computer reset mode. In the computer mode u is connected to the integrator developing x. The resulting system is analyzed and shown to be easily stabilized.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 20, 1963
- Accession Number
- AD0410448
Entities
People
- Albert I. Talkin
Organizations
- Harry Diamond Laboratories