Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I want to represent Euler-Lagrange equations in a (sparse) matrix form, such that; Az=b.

(in order to improve performance when solving).

I know A should be diagonal block, very large, and sparse.

my equations are:

1. -ψ'(Ix*Iz) + [itex]\gamma[/itex]ψ'(Ixx*Ixz + Ixz + Ixy*Iyy) - βη(ψ'(u-u1).

2. -ψ'(Iy*Iz) + [itex]\gamma[/itex]ψ'(Iyy*Iyz + Ixy*Ixz) - βη(ψ'(v-v1).

η - means some kind of neighboring of u.

I know it should looks something like:

Az=b:

where

z = [u1 v1 u2 v2 ....un vn]τ (column vector).

b = - [ψ'xz + βηU IxIz + βηV ... ] (Alternately) --> I'm not so sure here..

and A is very large, and saprse, of size 2*(n*n) - where n is the number of values I have.

Are z and b correct ? How should A be constructed ?

Thanks

Matia

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Euler-Lagrange as a Sparse matrix

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for Euler Lagrange Sparse |
---|

I Derivative of Euler's formula |

A Maximization problem using Euler Lagrange |

I Euler Lagrange formula with higher derivatives |

A Derivation of Euler Lagrange, variations |

I Rigorously understanding chain rule for sum of functions |

**Physics Forums | Science Articles, Homework Help, Discussion**