Continuous system & Infinite d.o.f.

AI Thread Summary
A continuous system indeed has infinite degrees of freedom, but it is governed by a single partial differential equation (PDE) rather than multiple ordinary differential equations (ODEs). This is because the behavior of continuous systems can be described by a single equation that accounts for all points in the system simultaneously. The confusion arises from equating degrees of freedom directly with the number of governing equations, which is not applicable in continuous cases. In essence, while there are infinite degrees of freedom, they are encapsulated within one PDE. Understanding this distinction clarifies the governing dynamics of continuous systems.
koolraj09
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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.
 
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