Introduction To Constrained Dynamics: Resources & Sources

[Narasoma]

I need a brief introduction to constrained dynamics. Any article, paper or books will help. If you know sources related to that matter, please tell me...

 

[Dr.D]

When you say "constrained dynamics," what do you mean? Dynamics with one or more forces of constraint acting?

 

[Simon Bridge]

You realize that there is a great deal on this topic - could you add some <ahem> constraints to your requirements so we can narrow it down?
I mean, they are all "sources related to the matter" ... there's literally millions of publications that fall under, "any article, paper, or books".

What do you need this for? What we give you will be different if you need it for a job or for self-study... or something else.
It will also be different depending on your current education level, and if you need a computer-oriented introduction or a more analytical/theoretical introduction.

At college level ... The Springer series is usually good ... https://link.springer.com/book/10.1007/BFb0036225 ... but I would usually suggest soething shorter and cheaper like https://www.cs.cmu.edu/~baraff/pbm/constraints.pdf and online lecture series for the first look, then you narrow down your search from there.

 

[Narasoma]

When you say "constrained dynamics," what do you mean? Dynamics with one or more forces of constraint acting?

I understand "basic" Lagrangian and Hamiltonian mechanics, but I don't get the understanding about constraint. Constraint of the first kind, constraint of the second kind... What is that?

 

[Narasoma]

You realize that there is a great deal on this topic - could you add some <ahem> constraints to your requirements so we can narrow it down?
I mean, they are all "sources related to the matter" ... there's literally millions of publications that fall under, "any article, paper, or books".

What do you need this for? What we give you will be different if you need it for a job or for self-study... or something else.
It will also be different depending on your current education level, and if you need a computer-oriented introduction or a more analytical/theoretical introduction.

At college level ... The Springer series is usually good ... https://link.springer.com/book/10.1007/BFb0036225 ... but I would usually suggest soething shorter and cheaper like https://www.cs.cmu.edu/~baraff/pbm/constraints.pdf and online lecture series for the first look, then you narrow down your search from there.

Maybe some books of classical mechanics with constraints for undergraduate theoretical physics student will help. Thanks.

 

[Simon Bridge]

Maybe some books of classical mechanics with constraints for undergraduate theoretical physics student will help. Thanks.

Did you have a look at the suggestions?

Senior undergrad would include Lagrangian mechanics and the principle of least action - that what you are looking for?
Next level down would basically be differential equations with boundary/initial values.
Basically all the physics you do in secondary school is classical mechanics with constraints... it's just not formally delivered that way.
If you want to know this stuff for a course you are taking at college level, then you should use the textbook for the course.

To give you an idea of what is involved - see Susskind's lectures on classical mechanics.

... see what you think.

 

[vanhees71]

I understand "basic" Lagrangian and Hamiltonian mechanics, but I don't get the understanding about constraint. Constraint of the first kind, constraint of the second kind... What is that?

The original sources are (open access)

https://cms.math.ca/10.4153/CJM-1950-012-1

and (unfortunately behind a paywall)

https://www.jstor.org/stable/100496?seq=1#page_scan_tab_contents