Lagrangian Mechanics: A pendulum swinging from a moving horizontal cart.

Рет қаралды 14,118

3 жыл бұрын

I call this the "jiggle" pendulum. It's a mass hanging down from an oscillating cart.
Here is the code
trinket.io/glowscript/f27133ec19
Introduction to Lagrangian Mechanics
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Пікірлер: 19

@alakis 3 жыл бұрын

I should be studying but here I am, watching random KZfaq videos.

@gbpferrao 2 жыл бұрын

I'm a architecture student and i should be doing an essau about the main features of architecture design throughout history, though I am here amazed by lagrangian mechanics

@DotPhysics 2 жыл бұрын

Me too

@elir9077 2 жыл бұрын

Thanks for all the great videos. Is it also possible to do this in polar coordinates?

@navneetmishra3208 3 жыл бұрын

Can u please derive an equation for a ball that is attached with massless string to a circular rod of some radius and the ball is making whirlpool motion around the circular rod if some tangential velocity is given to the ball. I am not so good at this kind of questions and in lockdown your videos are helping me a lot. and ur python code is a cherry on a cake. perfect!

@RickyKwokMath 3 жыл бұрын

Amazing. I'm sure you've already thought about this, but what does the Lagrangian look like (and simulation) if you assume the cart is on a frictionless plane so that the frequency (omega) is also time dependent with an initial condition of some theta between 0 and pi/2?

@imael_8532 3 жыл бұрын

Hi, sorry to bother you! Firstly, the video is truly amazing. I loved my university course about Lagrangian mechanics and I've never thought to use programming to create a model of the systems we studied. Let's get to the question: I've never seen a Python program before (in my uni we studied a bit of C++), so I have a question about it. What does the stick.axis part do? I mean, what's the value or variable associated with it? Thank you, sorry for my bad English! :)

@DotPhysics 3 жыл бұрын

stick is the name of the object "stick" - it's an object type cylinder. The axis is a vector from one end to the other - here is the info on cylinders - www.glowscript.org/docs/VPythonDocs/cylinder.html

@SpinoStirk Жыл бұрын

When taking the partial of L with respect to θ, should'nt it be (θdot)² instead of (θdot) since you're derivating cosθ ?

@MG-yg3fn 2 жыл бұрын

Amazing.

@Stuk4s 3 жыл бұрын

Super cool

@Fouriersoft 3 жыл бұрын

You mentioned at 1:25 your cart moves back and forth according to time, and not according to the position of the pendulum mass... How does that make sense? If you remove the pendulum, the cart will not oscillate, so surely the carts position is dependent on theta, the relative position of the pendulum mass?

@DotPhysics 3 жыл бұрын

It's like a driven cart at the top with a motor. It's motion does not change because of the swinging mass. We could make another case with a free car at the top - but that would be a different solution.

@Fouriersoft 3 жыл бұрын

@@DotPhysics oh I see, I must have missed that part. Thank you

@JasonJin3 2 жыл бұрын

Amazing! Why was kinetic energy of jiggle not considered?

@DotPhysics 2 жыл бұрын

there is an external force on the pivot point -since the point moves, the external force does work on the system to change the energy.

@science8544 2 жыл бұрын

why is Y = -Lcos(theta) and not Y = L-Lcos(theta) ?

@marwasaif1260 Жыл бұрын

Why do we only have one degree of freedom?

@DotPhysics Жыл бұрын

The position of the cart is set by the oscillation function - it is not free to move however it likes. That leaves just one degree of freedom. Don't confuse this with the similar problem that has a cart on a track that's free to move and a pendulum swinging underneath - that would have 2 degrees of freedom (I might already have a video on this version).