Classical Mechanics Lectures 07 | Scleronomic, Rheonomic constraints, Monogenic Systems, Phase Space

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3 жыл бұрын

Classical Mechanics Lectures by Sivakumar for MSc Physics full course - Lecture 07 - We learn the formal way to write the constraints and understand the scleronomous constraints. Then we define monogenic systems followed by an introduction to the phase space.
Recommended Readings:
Thornton and Marion. Classical Dynamics of Particles and Systems.
H. Goldstein. Classical Mechanics.

Пікірлер: 187

@ProfSivakumarRajagopalan 3 жыл бұрын

MSc level Classical Electrodynamics Playlist kzfaq.info/sun/PLtUBquogGkRv5CME__m2oudBqW3_ffv33 MSc level Vector space and Hilbert space for Quantum mechanics Playlist: kzfaq.info/sun/PLtUBquogGkRuZH23UO-8AWR4dzcu-La8_ MSc level Classical Mechanics Playlist kzfaq.info/sun/PLtUBquogGkRukyAAWOmq2LmQx8Yf9H_3E BSc level Electricity and Magnetism Playlist kzfaq.info/sun/PLtUBquogGkRu66Kqgs3HsEpHEP6IA8oQ7 (a) Choose 1080p resolution when viewing the video on 10-inch tablet. (b) Use 4K resolution when viewing on laptop/desktop. (c) Keep the volume of the audio less than 93%. Otherwise, the sound may get distorted. (d) Use headphones to experience superior audio quality.

@MuhammadIsmail-oj3sj 3 жыл бұрын

Best teacher on KZfaq for classical mechanics God bless you for helping us

@ProfSivakumarRajagopalan 3 жыл бұрын

Thank you, and best wishes.

@krushnachandrashankhua637 3 жыл бұрын

Perhaps this is the best vedio on KZfaq for holonimic and non-holonomic constraint.Mind blowing explanation sir 😇

@ProfSivakumarRajagopalan 3 жыл бұрын

Students like you keep the teachers active... In a way, I learn how much to explain after interacting with students. Thank you.

@elamvaluthis7268 2 жыл бұрын

Really great 😁😁😁.painstakingly explaining things very rare kind sincerity always pays.

@pranavbhaskaran5 3 жыл бұрын

In case of moving pivot example Can rheonomous constraints be converted to scleronomous if i observe the system from the rest frame of reference of the pivot? Shortly, can constraint types be changed through appropriate Galilean transformations?

@ProfSivakumarRajagopalan 3 жыл бұрын

Good thought. Yes, partly right... but vibrator (moving pivot) is not the one with uniform velocity. So, this is a non-inertial frame. Hence it may not become scleronomous.

@saadhassan8813 9 ай бұрын

You are great teacher sir!!

@gunjaranilakra2021 2 жыл бұрын

Nicely explained the concepts sir, Thank you.

@NithunaN 2 жыл бұрын

Clearly explained sir

@theerdhathulasi6875 2 жыл бұрын

Veru helpful class. Thank you sir♥️

@adwaitm6871 2 жыл бұрын

Thank you, sir.

@soundharryaamanoharan6940 2 жыл бұрын

Thank you Sir!

@minam__mm 2 жыл бұрын

Thank You Sir.

@V15H4L_4RJUN 2 жыл бұрын

Thank you sir !!

@nivetham9534 2 жыл бұрын

Thank you sir!

@mohammadsuleman3058 3 жыл бұрын

Very help full plz sir upload vadios frequently thanks sir

@ProfSivakumarRajagopalan 3 жыл бұрын

Ok, I will do the best.

@abhijitsethi9792 2 жыл бұрын

Thanks a lot sir

@karthikas6911 2 жыл бұрын

Thank you sir ✨

@vishwa9713 2 жыл бұрын

Thank you sir...

@deepaks7015 2 жыл бұрын

Thank you sir.

@tanyajaiswal08 2 жыл бұрын

Very nice explaination Sir..

@ProfSivakumarRajagopalan 2 жыл бұрын

Thanks for liking. Best wishes.

@ansifhussainvk6404 2 жыл бұрын

Thank you sir 👍

@sureshthsngsrsjsn 2 жыл бұрын

Respected sir before entering phase space diagram , v plot x vs t from that diagram take slopes it gives the value of DX/ DT = xdot. My doubt is slope value and our xdot value different r not why ?

@sarahsalter9096 2 жыл бұрын

Thank you sir😃

@tayyabahaider3872 3 жыл бұрын

Thank you so much sir..your videos are so helpful

@ProfSivakumarRajagopalan 3 жыл бұрын

Glad to hear that and welcome.

@girisankar2474 2 жыл бұрын

Thank You Sir

@nivedha3785 2 жыл бұрын

Thanks sir 😄

@naincykiro2940 2 жыл бұрын

Thankyou Sir

@siddharth6633 3 жыл бұрын

Sir, the diagram of phase space shows that for one position, there are two corresponding values of it's velocities. So is the particle moving along the same path twice so that it has two different velocities at one position?

@ProfSivakumarRajagopalan 3 жыл бұрын

Good observation. To answer, we have to consider the time, which is represented by arrows. For closed and overlapping paths such as circles, the particle crosses the same position at two different times. They have two different velocities at the same position, but it happens at two different times. Therefore no confusion. Regards and Best wishes.

@siddharth6633 3 жыл бұрын

@@ProfSivakumarRajagopalan all clear sir thank you

@pratyushmohanty6185 2 жыл бұрын

Thanks sir

@physics1789 2 жыл бұрын

Sir, isn't the entire idea of potential there for conservative systems? Is it possible to have a potential function when the force is non conservative? (41:12)

@ProfSivakumarRajagopalan 2 жыл бұрын

When the force is non-conservative, then, it cannot be equivalently represented by a potential function.

@kisore20gp 2 жыл бұрын

Thank u sir

@ranithalder3423 2 жыл бұрын

Clear sir

@Epitome2 2 жыл бұрын

Professor at 19.00 you say that we dont know equation of constraint. But we known the frictional force if mass and mu is given. Then how can it be unknown ?

@ProfSivakumarRajagopalan 2 жыл бұрын

We have limited experimental values for the coefficient of friction mu. But in general, the friction between any two arbitrarily moving objects is not known. Whenever this happens, we can classify it as non-holonomic.

@anjalim5135 2 жыл бұрын

thanku sir

@amudhanm2699 2 жыл бұрын

Tq sir

@tushar9723 3 жыл бұрын

Sir very nice explanation,But I just confused on a small topic. In your prev. video(Ref.-Classical Mechanics Lecture 06, 1 hrs 05 min.) You said when time is explicitly present it is Non holonomic system,but in this lecture you said Rheonomous constraints are subpart of Holonomic constraints even when it depends on time. How this is possible sir? Please explain.

@ProfSivakumarRajagopalan 3 жыл бұрын

A constraint is classified as non-holonomic if the constraint equation is unsolvable for one or the other reason. This situation leads to the non-integrability of the dynamical system. However, the Rheonomous constraint is one where explicit time dependence complicates the mathematics but still solvable, which means the dynamical system is integrable.

@tushar9723 3 жыл бұрын

@@ProfSivakumarRajagopalan Thank you so much sir for clarification.

@ishratunnisa1898 Жыл бұрын

Sir will u plz upload lectures on quantum mechanics for MSC ist sem

@nsumanth18 2 жыл бұрын

Hello sir! Your explanations are really good and it would be fault from my side if such a good teaching is not appreciated. However, I have this doubt that when we consider the generalized coordinates or state space or even Lagrangian function, why do we consider it as function of q(dot) as well. My biggest confusion that still persist, is that isn't the q(dot) dependent on q( as q_dot is the time derivative of q) I have heard the reasoning that says the reason why they are independent is because say you know position then you have no idea of the velocity at that position, which makes sense but not satisfactory to me( may be I have not understood that properly), because my doubt is that, suppose you have a table for different x for different time t, and you plot a graph out of it. Now using the graph you can calculate the velocity at each point since it's just the slope right! So how is velocity not dependent and an independent variable! Can you please help me with that confusion? Thank you in advance!

@ProfSivakumarRajagopalan 2 жыл бұрын

Consider a ball rolling on a horizontal straight line. As the ball moves, you can measure the position of the ball at various times. Here, dx/dt gives qdot. Let the second example be a simple pendulum. You start the oscillations by giving the bob a known push (velocity) when it is at its equilibrium position (theta = 0 or equivalently q = 0). This means you know that qdot = C at q=0. In such situations, the first example idea will not work. Here, the set (q, qdot, t) is treated as the independent variables and solve for q as a function of time. This second example is more practical than the first example. Hence, we start constructing the Lagrangian as a function of (q, qdot, t).

@nsumanth18 2 жыл бұрын

@@ProfSivakumarRajagopalan Really grateful to your reply but Sir, I understood till qdot=C at q=0, but after that how are you concluding that they are two independent variables, that is still not clear to me! Can you please explain a little more!

@ProfSivakumarRajagopalan 2 жыл бұрын

At the time of the starting of the experiment, we have t=0 in our stop clock. At that time, the bob is located at its equilibrium position q=0. In such a situation, we apply a constant (C) initial velocity to the bob. So, we have the set of variables t=0, q=0 and qdot=C, which are all independent of each other. Here "independent" means you can fix each of the three values as you wish. For instance, your initial push need not necessarily be at q=0 but at any other position q=qo. Similarly, the stop clock need not be t=0 when you start the experiment, but rather, it can show any other time t=to when you begin the experiment. Under this condition, you can set the initial velocity to a constant D instead of C. So, changing one variable value does not affect the other two variables. This is what we mean by "independent variables".

@nsumanth18 2 жыл бұрын

@@ProfSivakumarRajagopalan Yeah understood sir! Thank you so much sir! Pleasure!

@ankitmishra2723 2 жыл бұрын

@@ProfSivakumarRajagopalan thanks sir,it it was surely a confusion but simple pendulum example clarified all.

@rohanmathew5728 2 жыл бұрын

Professor…still not clear with the idea of classifying a constraint that depends explicitly on velocity as being non-holonomic although it maybe written in the form of an equation rather than an inequality.

@ProfSivakumarRajagopalan 2 жыл бұрын

Let the constraint equation be an equality relation. If this equation is not solvable for some reason, then we classify the constraint as non-holonomic. Generally, this difficulty comes due to velocity, velocity-dependent potentials, or time-dependent potentials.

@rohanmathew5728 2 жыл бұрын

@@ProfSivakumarRajagopalan Alright...maybe the successive videos would make this argument clearer.. thankyou professor..

@ProfSivakumarRajagopalan 2 жыл бұрын

A dynamical system which is not solvable is known as non-holonomic, which is again equivalently known as non-integrable. These are equivalent or synonyms.

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