Are there real-world applications of Hamilton's Principle in mechanics?

  • #1
Trying2Learn
375
57
TL;DR Summary
From the schematic to the real.
Goooood Morning all!

I am going through a few problems in advanced dynamics with Hamilton's Principle.

Skjermbilde.JPG


One of them is shown above (this is NOT a question about the solution)

The spring constants, damping, mass, force, are all given. So, too, is the constraint: large disk rolls without slipping.

My question is this: Does such a mechanical device exist?

I suppose one could replace the "rolling without slipping" constraint with "rack and pinion" gear set.

  1. But is this specific schematic representative of some real device?
  2. And, more generally, but just as important to me: as I go through such examples, how can I find out if the schematics for the varied problems exists?
  3. Or should I content myself with realizing that these are indeed simple schematics to learn the language of how to apply Hamilton's Principle? (much like found in electrical circuitry examples)
 
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  • #2
Trying2Learn said:
TL;DR Summary: From the schematic to the real.

My question is this: Does such a mechanical device exist?
I am not sure about semantics of "exist" you use. The system seems reasonable and realizable at least theoretically to me.
 
  • #3
anuttarasammyak said:
I am not sure about semantics of "exist" you use. The system seems reasonable and realizable at least theoretically to me.
No, what I mean is: is it a schematic from a useful mechanism
 
  • #4
Trying2Learn said:
TL;DR Summary: From the schematic to the real.

Goooood Morning all!

I am going through a few problems in advanced dynamics with Hamilton's Principle.

View attachment 332084

One of them is shown above (this is NOT a question about the solution)

The spring constants, damping, mass, force, are all given. So, too, is the constraint: large disk rolls without slipping.

My question is this: Does such a mechanical device exist?

I suppose one could replace the "rolling without slipping" constraint with "rack and pinion" gear set.

  1. But is this specific schematic representative of some real device?
  2. And, more generally, but just as important to me: as I go through such examples, how can I find out if the schematics for the varied problems exists?
  3. Or should I content myself with realizing that these are indeed simple schematics to learn the language of how to apply Hamilton's Principle? (much like found in electrical circuitry examples)
Looks pretty much like that you could build it. Why shouldn't it be possible?
 
  • #5
vanhees71 said:
Looks pretty much like that you could build it. Why shouldn't it be possible?
Yes, I know I can build it, but that is not the question.

I see all these examples in a textbook on Hamilton's Principle.

With some of them, I want to motivate the students by saying

"Yes, we could build it, but it would not be purposeful/useful."

I am trying to find out if this mechanism actually does serve a real world purpose.

In fact, I am hoping to do that for MANY problems such as these.

Or, must I content myself, that if I add more springs or dashpots, all am doing is giving varied problems that have no real-world counterpart, but are ONLY useful to learn the language of Hamilton's Principle (a worthy endeavor, nonetheless).
 
  • #6
Hm, it's just to train the students to solve non-trivial mechanical problems. I don't know, what you mean by "real-world purpose".
 
  • #7
By "real world purpose" I only meant: "can I say to the students: yes, this is an ideal problem to learn the workings of HP, but in THIS particular case, THIS mechanism is also used for this purpose."

But I am beginning to think most of the examples given in textbooks that teach HP, are indeed didactic constructions and not related to actual useful mechanisms.
 
  • #8
A nice example is the gyrocompass at the very end of the mechanics lecture, i.e., the motion of a (restricted) top on the rotating Earth ;-).
 
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