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Research Article

Year : 2016 | Volume: 2 | Issue: 1 | Pages: 7-11

Modelling of two Interconnected Spring Carts and Minimization of Energy

Muhammad Raheel Mohyuddin1*, Jamshaid ul Rahman, Naveed Anjum, Rehan Butt2

DOI: 10.18831/djmaths.org/2016011002

Corresponding author

Muhammad Raheel Mohyuddin*

Department of Mathematics and Statistics, Caledonian College of Engineering, Oman.

  • 1. Department of Mathematics and Statistics, Caledonian College of Engineering, Oman.

Received on: 2015/12/10

Revised on: 2016/01/10

Accepted on: 2016/01/20

Published on: 2016/01/31

  • Modelling of two Interconnected Spring Carts and Minimization of Energy, Muhammad Raheel Mohyuddin, Jamshaid ul Rahman, Naveed Anjum, Rehan Butt., 2016/01/31, DJ Journal of Engineering and applied Mathematics. , 2(1): 7-11, http://dx.doi.org/10.18831/djmaths.org/12016011002.

    Published on: 2016/01/31

Abstract

Focus is to form a mathematical model for interconnected spring carts to minimize the energy using Powell’s method of minimization. Expressing the energy of a surface in terms of its local deformation, local force on the surface is given by differentiating the energy with respect to position that gives an equation. The modelled equations make a system that has been converted in to a biquadratic function and used to minimize the energy to save the life of spring in the best method of optimization. The Powell’s method is given in detail and compared with Downhill Simplex method.

Keywords

Mathematical modelling, Interconnected spring carts, Ordinary differential equation, Derivative-free optimization, Powell’s method.