Small oscillations

1. Sep 3, 2012

saravanan13

Dear friends,

In small oscillation problem of classical mechanics, the generalized force is zero (Eq. (6-1)) of the Goldstein book.
The suffix 'i' represent the the particle number or coordinate?
In Eq. (6-3) of the same problem the summation convention is used. what is the purpose of using it?
In Eq. (6-5), the mass of the system m_{ij} is used.
Whether it indicates that mass of the system varies with space?
Why the mass is expanded in terms of Taylor series?

Ref: Classical mechanics by Goldstein.
Thanks in well advance.