# Help would be realy good now.

1. Aug 21, 2004

### mooberrymarz

hey ppl! have just started a course in lagrangian mechanics and it hasnt been the easiest thing. Ahemm, Anywayz we have a assigment to hand in I just dont know how to do these questions. You have to
1. Name cartesian co-ordinates which fully specify the position of all the moving masses in the system.
2. Obtain expressions giving each of the cartesian co-ordinates as functions of the genralised co-ordinates.

]Could any of you show me how to do these 2 and I will try do the rest by myself.]

a. A plastic knife flying through the air
b.A piece of chalk rolling without slipping inside a stationary cardboard roll, but with slippage allowed between the chalk and the board.

Thanx. moo

2. Aug 21, 2004

### ArmoSkater87

Be more specific, what do you mean by cartesian co-ordinates? Explain the situation clearly, and exactly what your assignment is, its hard to help when only a couple of questions are known from an entire assignment.

Is this the situation that the two questions apply to?

3. Aug 21, 2004

### mooberrymarz

I typed out exactly what my lecturere gave us. You should do 1.) and 2.) for a) and b). In other words for the two cases propose generalised coordinates that directly express the system's position using the minimum amount of parameters. I dont really get what he wants myself.

4. Aug 21, 2004

### marlon

I think mooberrymarz means you gotta choose a referenceframe in which the coordinates are as simple as possible.

But what about them generalized coordinates, huh ???

regards
marlon

Last edited: Aug 21, 2004
5. Aug 21, 2004

### HallsofIvy

For a "plastic knife", that is, a rigid body with a length much greater than the other two dimensions, you could do this: choose a point at one end and record its (x, y, z) coordinates. To find the coordinates of any other point, you will need to know its distance from that recorded point as well as the angles the line between them makes with the x, y, z axes (Those are not independent so you really only need two angles). That is, this is a 6 dimensional problem. "Generalized" coordinates means that you must include momenta as independent coordinates.

6. Aug 21, 2004

### robphy

As some have said, "cartesian coordinates" are x,y,z coordinates that locate the object. These are coordinates in a "configuration space".

"Generalized coordinates" are another set of "configuration space" coordinates.
For example, it may be that there is a more convenient set of coordinates, or there may be some constraints on the cartesian coordinates.

A useful question to keep in mind is "How many [configuration] degrees of freedom does the system have?"
A particle confined to a circle has one degree of freedom, although one might use two [obviously not independent] cartesian coordinates to describe it.

http://www.sydgram.nsw.edu.au/CollegeSt/extension/lagrangian/lagrang.pdf [Broken]
(p 26 may be enlightening)

Last edited by a moderator: May 1, 2017
7. Aug 22, 2004

### mooberrymarz

Thanx you guys! : )

8. Aug 23, 2004

### Math Is Hard

Staff Emeritus
Hey moo - good luck on the assignment. It's nice to see you around PF again.

9. Aug 23, 2004