Continuous system & Infinite d.o.f.

[koolraj09]

Hi All.
I may sound weird and I know I am wrong somewhere. But a little explanation would really help.
A system with 1 degree of freedom(d.o.f) has 1 governing differential equation. Similarly a system with 2 d.o.f has 2 (coupled) differential equations and so on. But a continuous system has infinite d.o.f so, it should have infinite differential equations. In contrast it has only one governing differential equation.
What is wrong in the above logic?
Thanks.

 

[Filip Larsen]

In a space-continuous system you typically end up with partial differential equations (PDE) instead of the ordinary differential equations (ODE) you get when your state variables are discrete. See [1] for some examples.

[1] http://en.wikipedia.org/wiki/Partial_differential_equation