Continuous system & Infinite d.o.f.

In summary, the conversation discusses the number of governing differential equations in systems with different degrees of freedom. It is noted that a continuous system typically results in partial differential equations instead of ordinary differential equations. The conversation also refers to a resource for examples of these types of equations.
  • #1
koolraj09
167
5
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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  • #2

1. What is a continuous system?

A continuous system is a physical system that can be described by continuous functions or equations. It is characterized by having an infinite number of degrees of freedom, meaning that it has an infinite number of possible states or configurations.

2. What are degrees of freedom in a system?

Degrees of freedom (d.o.f.) refer to the number of independent parameters or variables that are needed to describe the state or behavior of a system. In the case of a continuous system, this number is infinite, as there are an infinite number of possible states or configurations.

3. How are continuous systems different from discrete systems?

Continuous systems are different from discrete systems in that they can be described by continuous functions or equations, while discrete systems can only take on a limited number of values or states. Continuous systems also have an infinite number of degrees of freedom, while discrete systems have a finite number of degrees of freedom.

4. What are some examples of continuous systems?

Some examples of continuous systems include a vibrating string, a pendulum, a mass-spring system, and a fluid flow system. These systems can be described by continuous equations and have an infinite number of degrees of freedom.

5. How are infinite degrees of freedom handled in scientific research?

Infinite degrees of freedom in a system can be challenging to handle in scientific research. One approach is to use simulations or mathematical models to approximate the behavior of the system. Another approach is to reduce the system to a finite number of degrees of freedom by using simplifying assumptions or approximations.

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