Continuous system & Infinite d.o.f.

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SUMMARY

A continuous system is characterized by having infinite degrees of freedom (d.o.f), yet it is governed by a single partial differential equation (PDE), unlike discrete systems which have multiple ordinary differential equations (ODE). This distinction arises because continuous systems model variables that change smoothly over space, leading to PDEs that encapsulate the behavior of the entire system rather than individual components. The confusion stems from equating the number of d.o.f directly with the number of governing equations, which is not applicable in the context of continuous systems.

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  • Understanding of degrees of freedom (d.o.f) in mechanical systems
  • Familiarity with ordinary differential equations (ODE)
  • Knowledge of partial differential equations (PDE)
  • Basic concepts of continuous versus discrete systems
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  • Study the formulation and applications of partial differential equations (PDE)
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Students and professionals in engineering, physics, and applied mathematics who are interested in the behavior of continuous systems and the mathematical frameworks that describe them.

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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