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Hi,

I'm a bit confused wit the concept Configuration Space.

First, the professor defined generalised coordinates as such:

U got a system of n particles, each particle has 3 coordinates(x,y,z), so u got 3n degrees of freedom.

If the system has k holonomic constraints, u got 3n-k degrees of freedom.

Instead of working with cartesian coordinates, we now define a new set of coordinates q

These are the generalised coordinates of the system,3n-k in total.

I get this.

Then a little bit further, when explaining Hamilton's Variatonal Principle, he defines a Configuration Space.

"The configuration space of a system is a 3n-k dimensional space with the generalised coordinates on the coordinate-axes."

So far, so good.

On the reference list of this course,Classical Mechanics of Goldstein is listed.

First page of the second chapter of Goldstein:

This n-dimensional space is therefore known as the configuration space...

In classical mechanics from Kibble, I didn't even found such thing as config space.

Also, on the internet I've found another course of Classical Mechanics:

http://www.phys.ttu.edu/~huang24/Teaching/Phys5306/CH2A.pdf" [Broken]

There they say

Also, there's a little graph with on the horizontal axis q1 and on the vertical axis q2, but there are n dimension, according to their course !!!

But for the axes only q1 and q2 is used, so why not qn-1 and qn.

But a graph with only two axis, is 2-dimensional right?

It is not ndimensional

See my frustration here?

Please help me.

I'm a bit confused wit the concept Configuration Space.

First, the professor defined generalised coordinates as such:

U got a system of n particles, each particle has 3 coordinates(x,y,z), so u got 3n degrees of freedom.

If the system has k holonomic constraints, u got 3n-k degrees of freedom.

Instead of working with cartesian coordinates, we now define a new set of coordinates q

_{1},q_{2},..,q_{3n-k}.These are the generalised coordinates of the system,3n-k in total.

I get this.

Then a little bit further, when explaining Hamilton's Variatonal Principle, he defines a Configuration Space.

"The configuration space of a system is a 3n-k dimensional space with the generalised coordinates on the coordinate-axes."

So far, so good.

On the reference list of this course,Classical Mechanics of Goldstein is listed.

First page of the second chapter of Goldstein:

This n-dimensional space is therefore known as the configuration space...

In classical mechanics from Kibble, I didn't even found such thing as config space.

Also, on the internet I've found another course of Classical Mechanics:

http://www.phys.ttu.edu/~huang24/Teaching/Phys5306/CH2A.pdf" [Broken]

There they say

Here they say n generalised coordinates in n dimensional space, not like according to my professor 3n-k dimensions with 3n-k generalised coordinates!Meaning of “motion of system between time t1 and t2”:

• A system is characterized by n generalized coordinates

q1,q2,q3,..qn.

• At time t1: q1(t1),q2(t1),..,qn(t1) represent a point in the ndimensional

configuration space.

• As time goes on, the system point moves in configuration

space tracing out a curve, called the

path of motion of the system.

• At time t2: q1(t2),q2(t2),.. ,qn(t2)

represent another point in the ndimensional

configuration space.

Also, there's a little graph with on the horizontal axis q1 and on the vertical axis q2, but there are n dimension, according to their course !!!

But for the axes only q1 and q2 is used, so why not qn-1 and qn.

But a graph with only two axis, is 2-dimensional right?

It is not ndimensional

See my frustration here?

Please help me.

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