Lagrange Equations: Multiple Particles and Constraints

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In this video on Analytical Mechanics, I discuss extensions to the Lagrange equations when working with systems of multiple particles or when constraints are involved. I also discuss constraints in classical mechanics, including holonomic (scleronomic + rheonomic) and non-holonomic constraints.
I finish the video with a strategy on how to solve problems involving multiple particles and constraints using the Lagrange equations, which is a nice segue to my next video, where I solve an actual Action Problem.
Questions/requests? Let me know in the comments!
Prereqs: The videos before this one on my playlist - • Analytical Mechanics
Lecture Notes: drive.google.c...
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Twitter: / facultyofkhan
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Опубликовано:

29 сен 2024

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Комментарии : 24

@FacultyofKhan 6 лет назад

A comment that I get quite a bit (both here and in real life) is that I sound like a robot. Because of this, I'm often left to question my identity: am I really an Android or am I a real person? After becoming inspired by ze masterpiece zat is Detroit: Become Human, I've decided to pose this question to my viewers: what am I? [△] Human [◻] An Android who Became Human [O] An Android who always accomplishes his Mission™

@Wompylulz 6 лет назад

◻

@TheBigWazowski 6 лет назад

Well if you are Connor... 0

@Nithesh2002 6 лет назад

That intro was scarily accurate

@46pi26 6 лет назад

I can't type those symbols, but I can say that I wouldn't mind you taking over the world to "save" humanity.

@ConnorMooneyhan1 6 лет назад

⬜ we all know it's true! (PS, love the name 😏)

@jackdeago3639 Год назад

Can you Complete this series

@XanderGouws 6 лет назад

Perkins: What's that? Connor: My name is Connor. I'm the android sent by Cyberlife.

@46pi26 6 лет назад

Intro makes sense. And honestly, your robotic voice is not only nice to listen to in an educational environment, but it also makes your jokes much more effective. Of course, not all jokes work well with monotone voice, just the well written ones.

@Wompylulz 6 лет назад

Really love this series! I've studied analytical mechanics at uni on a very VERY rigorous book: analytical mechanics by Fasano, Marmi, two Italian professors. It was sort of a pain but it was worth it. Still loving analytical mechanics

@sayanjitb 4 года назад

Dear sir, why the rolling ball on surface includes non- holonomic constraint is not apparent to me. Can anyone shortly express the idea! Thanks in advance

@yudhisthir7247 5 лет назад

Each and every video is so informative and fantastic that I enjoy like anything. Once again thankyou very much and god bless you.

@danparrott7570 Год назад

Hi do you have any links to explanations on how to incorporate multiple inequality constraints?

@Jhonjackdiab 6 лет назад

are you gonna do BBGKY Hierarchy?

@FacultyofKhan 6 лет назад

That's a very niche topic haha; if there's enough interest, I'll consider doing it later on, but not right now when I still need to start statistical mechanics.

@tomasrojas999 3 года назад

I'd say that for a free particle there would be 6 degrees of freedom since the velocities also should be counted as is in the phase space

@nellymadani1694 4 года назад

helped me so muchhh!! Thanks

@password6975 4 года назад

THANK YOU

@ArielSasson 5 лет назад

@mathislove3722 5 лет назад

What do you mean by writing z as a function of x and y on the sphere exactly? z is obviously NOT a function of x and y. For each x and y on the sphere, you get a pair of values for z that work, not just one z.

@floshey 5 лет назад

I am also confused by this.

@jakabbaZ 4 года назад

With the equation of a sphere, i.e. x^2+y^2+z^2=R^2 you can express f(x,y) = z, which in this case is just z^2 = R^2-x^2-y^2. Since you see that all the coordinates are squared, it essentially doesn't matter that you have "a pair of values". The pair of value happens to be the same values since z^2 > 0 for every value of z. This gives us the constraint which reduces the degrees of freedom.

@mbrusyda9437 3 года назад

@@jakabbaZ I think he's just being pedantic on the definition of function. A function is single-valued, so z is not a function of (x,y) since for a particular (x,y) z has 2 value

@jakabbaZ 3 года назад

@@mbrusyda9437 I suppose so. Pure mathematicians really don't like the way we physicists use mathematics sometimes. Although most of the times, like this one, we are doing nothing wrong, we take shortcuts to simplify the calculation. Sometimes even use wrong terms or do "illegal" things without altering the solution. For example, in differential calculus we often like to just multiply or divide ODE with dy or dx, when in fact dx/dy, also f'(x), is not a division. I guess in the end it's just harmless little banter between two fields of scientists.