one man

Alexey Ivanov

705 Reputation

14 Badges

8 years, 34 days
Russian Federation

Social Networks and Content at Maplesoft.com

Maple Application Center

MaplePrimes Activity


These are Posts that have been published by one man

       Calculation of RSCR mechanism as a  solution to underdetermined system of nonlinear equations.  

 

RSCR.mw 

https://vk.com/doc242471809_376439263
https://vk.com/doc242471809_408704758

RCCC mechanism
https://vk.com/doc242471809_375452868

      Method for solving underdetermined systems of nonlinear equations. The idea of the method is to find a connected subset of a set of solutions of the system by moving along this subset from one point in different directions. The direction of movement can be changed in each point.

      Very simple example of  single equation with three variables:

                                   (x1 ^ 4 + x2 ^ 4 - 2) ^ 2 + x3 ^ 4 - 1 = 0;

      From the point (0, -1.31607, 0) or (0, 1., 0) or any point if it is a solution, we first move for a variety of solutions along a curve parallel to the axis Ox3, and then from each point of this curve is moving in a direction parallel to x1Ox2 or vice versa. So we get all the solutions.
      This works for any space of any number of the equations when the number of equations is less than the number of variables.
underdetermined_system.mw

 

 

 

    Intersection of surfaces:

x3-.25*(sin(4*x1)+sin(3*x2+x3)+sin(2*x2))=0;  (1)

(x1-xx1)^4+(x2-xx2)^4+(x3-xx3)^4-1=0;          (2)   

   Surface (1) and a set of surfaces (2). Point (xx1, xx2, xx3) belongs to (1). Moving along the surface (1), we compute its intersection with the surface (2).
   The program is very simple and its algorithm can be used for many other combinations of equations.

intersection_of_surfaces.mw  

4 5 6 7 8 Page 6 of 8