Crashing a Basis

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2 total messages Started by Jeffrey Horn Mon, 10 Aug 1992 14:51

#226

Author: Jeffrey Horn
Date: Mon, 10 Aug 1992 14:51

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Given an m x n matrix with linearly independand rows ( n > m ) is there any
good way to find m columns that form an invertible submatrix?  Does anyone
know of any code that might do this? 

Given that it can be done, can one do it in a way that makes the resulting
m x m matrix as close to triangular as possible?  as sparse as possible?

Any comments, references or code is welcome.

Regards, 

Jeffrey Horn

Vibs. Solution Solvers ??

#227

Author: David Russell
Date: Mon, 10 Aug 1992 21:05

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2202 bytes

I'm not sure if this is the right group, but here goes.

    I am having stability problems with a basic nonlinear vibrational
problem. Can anyone suggest a good solution technique for the problem
presented below in a simplified form.

   M*Qdd + C*Qd + K*Q + J*l = F

  M = | M_rr  M_rq |   C = | C_rr  C_rq |   K = | 0  0    | 
      | M_qr  M_qq |       | C_qr  C_qq |       | 0  K_qq | 

  Where, r - rigid body and q - flexible modes. (d-time derivative)
Q - Generalized coordinates vector, rigid and flexible.
J - Constraint Jacobian, and l - Lagranges multipliers.
The matrices are exact for rigid body modes, and nonlinear in q.
Presently, I solve the following ODE, (simplified form),

  Vd=M^(-1)*[ F - C*V - K*Q - J*l ]
  V=Qd

Using IMSL, SLATEC, and ODEPACK routines, Runge-Kutta, Adams, and
Gears (BDF). All the routines can solve
for rigid problems or flexible problems, But have problems when
rigid and flexible modes are present.

The problems I am solving require the transient result.

WANTED: 1) A more appropiate ODE solver, prefferably canned.
        2) Other solution techniques/solvers.
        3) Advice on efficient use of the IMSL, SLATEC and ODEPACK
           routines.
        4) Advice on RKSUITE, I just downloaded it but haven't
           implemented it yet.
        5) A lot of similar work uses NEWMARK numerical integration.
           a) Is there a code for this somewhere.
           b) How easy is it to implement.
        6) Any additional advice.

Thanks in advance, If there is a large response I will summarize.

DMR  - russell@sun.soe.clarkson.edu

--
David M. Russell, Mechanical Eng. Dept.
Clarkson University, Potsdam, NY 13676
(315) 268-9806 
russell@sun.soe.clarkson.edu

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