The use of the reciprocals of positive and negative inertial functions in asymptotic modelling
Abstract
This paper shows how the recently introduced concept of positive and negative inertial functions in asymptotic modelling may be used effectively. Noting an almost linear variation of the natural frequency over a wide range of values of the reciprocal of the inertial parameter, the results presented show that both the natural frequencies of constrained systems can be calculated accurately using only moderately large artificial inertial parameters, e.g. which are only about 10 times that of the system mass and also that values about a million times more than this do not precipitate illconditioning when using 16 figure computer accuracy. This helps to minimize the chances of numerical problems occurring due to the limitation of machine precision.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 June 2006
 DOI:
 10.1098/rspa.2005.1643
 Bibcode:
 2006RSPSA.462.1909W
 Keywords:

 inverse inertia;
 artificial inertia;
 asymptotic modelling;
 illconditioning