Torsion: How curves twist in space, and the TNB or Frenet Frame

Рет қаралды 139,566

Күн бұрын

If you have a curve through space, torsion measures the degree to which the curve "twists". This is separate from how the curve "curves", which we saw was given by the curvature formula. In this video we will study the TNB or Frenet Frame given by three vectors, the Tangent, the principle Normal, and the new vector called the BiNormal vector. The Tangent and Normal Vectors define a plane and what Torsion measures is how that plane changes as you move along the curve.
TYPO: Near the beginning, the Normal Vector should be 1/k dT/ds. I forgot the 1/k, where k is the curvature.
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Пікірлер: 200

@andrewrich9396 4 жыл бұрын

The normal vector N is not dT/ds. Rather it is dT/ds normalized, that is, dT/ds divided by its norm. dT/ds = curvature times N. Another way of saying it is that N is dT/ds divided by the curvature. He has this right later on, but not at the beginning.

@andrewrich9396 4 жыл бұрын

@@DrTrefor Thanks for the nice video. I was looking for clips to show my multivariable calculus class to show visualizations of torsion and the Frenet-Serret frame.

@ConceptualCalculus 3 жыл бұрын

Someone points out an error, and Dr. Bazett pins the comment. He is far more concerned with making sure everyone understands the math correctly than with appearing to be perfect. He is my role model. I want to grow up to be Trefor Bazett. (I'm older than he is, so that might not work.)

@abbasbookwala 3 жыл бұрын

Yes, I too got a little confused due to this, but spending few minutes deriving it understood this small imperfection...thanks for the great video

@GregSpradlin 2 жыл бұрын

Thanks for pointing this out, and thanks to Dr. Bazett for fixing it and pinning this comment

@AkamiChannel 6 ай бұрын

@@ConceptualCalculusYes, unlike the "Professor Dave Explains" guy who is arrogant and does not take criticism well.

@shekhararya8284 3 жыл бұрын

One of the best examples of 'How complexity gets simplified'... Probably now I won't forget it Thank you sir

@narenmani07 9 ай бұрын

The quality of this content is unbelievable!

@ayushgupta17 3 жыл бұрын

I am a first year electrical engineering student , thanks for your well define explanation as well as animation too. LOVE FROM INDIA

@simonekentish7491 Жыл бұрын

I’m taking differential geometry now nearly 30 years after vector calculus and multivariable calculus. Your videos are saving me massive amounts of time getting reacquainted with topics.

@anisurrahaman4490 7 ай бұрын

What's your passion or doing job or study math till

@edwardlu1143 2 жыл бұрын

Your animation explains the concept better than the equations alone.

@m.a.a.v.4333 Жыл бұрын

Brilliant! You were able to explain in little less than 15 minutes what my teacher struggled to teach me for, what, two weeks already? I'm so incredibly glad I found your channel. You just got yourself a new sub.

@chakky1234 3 жыл бұрын

For a self learning student this amazing video will be a boon. Thank you sir.

@manojn2675 3 жыл бұрын

I'm searching for torsion lately but I didn't get any proper idea about torsion. But suddenly i see you video totally, it's awesome and i got idea properly. Thanks 👍

@renzostefanmp7937 3 жыл бұрын

Wow, I have just discovered this channel and I'm really excited. I'm going to watch all of the differential geometry videos and others. Thank you! Subscribed!

@omarayoubi8135 3 жыл бұрын

i felt some difficult , but i always appreciated how you get us your information no one like you , you are so special ❤

@jacklam5658 Жыл бұрын

I have been watching a lot of videos on youtube, your this video is the only one that tells me the underneath meaning of the binormal vector. All other videos just give the mathematical formula which have no added value than reading textbooks. You did help me a lot in my self study. Very Great Work ! Thank you so much ! Jack Lam from Hong Kong

@maxwang2537 4 жыл бұрын

Just had a revisit of differential geometry and it now became must easier and less daunting than it used to be. The animation/visualisation of the frame in this video is very helpful. Thanks for sharing. One more like.

@pavanajsridhar939 4 жыл бұрын

Thank you for your hard work for explaining such a beautiful concept!!

@user-pr9sg9ji8i 2 жыл бұрын

Stucked at these terms months sir, thank you for this great explanation. Won't forget for life

@thembamoloi583 3 жыл бұрын

Thank you for this masterpiece, I really wish I found your content last year before maybe I wouldn't have failed

@DrTrefor 3 жыл бұрын

Thank you, sorry to hear that!

@NepaltoMars 4 жыл бұрын

Amazing video. Thank you for putting your hardwork in explaining and making visualisation easier.

@hannananan9427 2 жыл бұрын

Thank you so much for this amazing explanation! Your videos keep blowing me away!

@dox1755 4 жыл бұрын

Your way of speech always got me nice video man !

@azbutiki 4 жыл бұрын

Thank you for answering our homework. ❤️

@shivkarj1456 3 жыл бұрын

I can't express how thankful I am for your videos!

@DrTrefor 3 жыл бұрын

Glad you like them!

@karnikavashistha9030 2 жыл бұрын

Couldn't find best then this to explain such topics. Tq for explaining it. 🙌

@ajeetkumar5453 4 жыл бұрын

Thanks. It helped me a lot! Have a beautiful maths day.

@romboom2405 3 жыл бұрын

Good morning Dr, Your videos are amazing to understand the non linear Euler Bernouilli beam theory as we use transformation matrices and curvatures rates to recover section deflections and their rates ! Amazing work !

@DrTrefor 3 жыл бұрын

Cool!

@alisiraydemir 2 жыл бұрын

Beautiful explanation... Thank you!

@daniacerna17 Жыл бұрын

Benditos sean los su títulos y a este maravilloso Dr. que comparte sus conocimientos. Solamente puedo decir Gracias, explica de maravilla un tema que me parece complicado y el cual a mi profesor de Dinámica no le entiendo nada.

@rahmatkhan3982 4 жыл бұрын

u made everything clear,thanks

@anthonyheak3479 8 ай бұрын

Very well explained professor!

@bahramashtiani2345 4 жыл бұрын

That was very nice, It helped me a lot!

@ConceptualCalculus 3 жыл бұрын

Excellent, as usual.

@georgepp98 4 жыл бұрын

Thank you for clarification !

@robertjr8205 Жыл бұрын

Seeing these visuals helps me so much more when understanding what I’m doing

@guruprasadg1097 4 жыл бұрын

Nice explanation.Great work

@maverickxrng606 4 жыл бұрын

Thanks a LOT ....there's only FEW english tutorials on KZfaq ...helped a lot ..tomorrow is my finals ...

@el_andrius 2 жыл бұрын

Thanks for such wonderful explanation

@sreelakshmisuresh7617 3 жыл бұрын

Great work!!!

@muratkaansenturk6080 4 жыл бұрын

Definitely the best !

@edu-express9050 5 ай бұрын

I didn't go to college today because I have watched your video. You brought the college in my room.

@AdityaKKannan Жыл бұрын

I love this video, Dr. Bazett is the goat

@MrPJBarney 3 жыл бұрын

Incredible! Thank you so much for producing this video. This video helped me understand tangent, normal, and binormal components for my Dynamics class. Take care. God bless. Jesus loves you.

@andrewkoulogeorge2569 3 жыл бұрын

please don't stop making content. u are a wizard

@DrTrefor 3 жыл бұрын

Never!

@joaomattos9271 Жыл бұрын

Excellent!!

@parkerhyde7514 4 жыл бұрын

Fantastic explanation

@Sorya-gf7qw 2 жыл бұрын

Thank you so much sir it aids my understanding of topic

@ryanward8117 4 жыл бұрын

Amazing work the visuals made the concept much easier to grasp

@kirtiparashar1726 3 жыл бұрын

Thank you so much 🙌🏻

@user-is9xe4cx1r 5 ай бұрын

Watched two times and saved it clearly in my minds. No need to racall.

@gourivigneshjawalkar1755 3 жыл бұрын

That was really amazing

@user-md4rq8td3t 8 ай бұрын

Really good!

@j.k.sharma3669 Жыл бұрын

What a greatly explaination of torsion

@shivamk3397 3 жыл бұрын

Awesome , keep it up.

@helinyolcu908 4 жыл бұрын

thank you so much, that helped me lot

@Abdoolkasim 3 жыл бұрын

Beautifully explained! Great!

@DrTrefor 3 жыл бұрын

Glad you think so!

@dhritiranjan9453 2 жыл бұрын

Best explanation.

@maheshd4566 4 жыл бұрын

i liked your explaination.

@xFullBusterGaming 2 жыл бұрын

Thank you !!

@yasinreza889 Жыл бұрын

You are awesome!

@mokshjain7120 2 жыл бұрын

Sir the graphics are very helpful in understanding the concept .. thanku😄😄

@larshaji6117 3 жыл бұрын

the best lesson I have seen ever, thanks

@DrTrefor 3 жыл бұрын

Thank you!!

@devubkumar4264 3 жыл бұрын

Thank you so much sir❤

@tarunsisodia9157 2 жыл бұрын

This video shows how beautiful Mathematics really is. P.S. Thanks Dr. Trefor

@AKlaus-hp3sd 3 жыл бұрын

Thank you sir, your teaching is great. Please sir, make a video on TORSORS.

@JeetkrishnaDas 4 жыл бұрын

Thanks for the video and clear explanation. I wanted to know how to transform TNB to Cartesian coordinate system.It is useful in the path planning of vehicles.

@mathveeresh168 2 жыл бұрын

your students are very lucky to have you as their professor

@aymmenbatool7254 3 жыл бұрын

How you got such a deep insight? I am amazed! A great teacher!!!!!!!

@DrTrefor 3 жыл бұрын

thank you!

@floatingbonesjournal 9 ай бұрын

Interesting. I'm studying w/Wolfram U's new course on multi-variable calculus. Wolfram Lecturer Tim mentioned the torsional component of curves. I don't believe he called it a BiNormal Vector; your explanation noting it was the cross product of the other 2 vectors was highly useful to understand. Torque with Viviani's Curve had gotten my attention before I understood any of the mathematics. There's a rope-movement exercise technique called RMT Ropes (AKA "Flow Rope") where the rope's centerline approximates Viviani's Curve. When up to speed, there is a significant amount of torque when the rope hits the ground in front of the body: rope-over-the-top. There's also rope-under-the-bottom torque when the rope hits the ground behind the body. These can be rather significant; the rope will make a noticeable bounce at these 2 positions. Significant energy is required to propel the rope over the head; this reactance can provide a significant fraction of that energy. I do not know about torques elsewhere in the cycle; I'll have to plot the torque of the curve... In any case, I highly recommend checking out this exercise/movement technique. We rarely access our pronators/supinators directly, and all the spiraling lines in the body (arm, torso, and legs) are intimately connected. This could bring some lively homework to a math class!

@jacobvandijk6525 4 жыл бұрын

Nice video, sir.

@user-jc4sm7cv9y Жыл бұрын

really helpful

@dawgkys 4 жыл бұрын

thank you man.

@joaomattos9271 Жыл бұрын

Muito bom (do Brasil)! Very good (from Brasil)!

@user-wp2pl8dx6s 2 ай бұрын

I love it so much! Can you share which software you use to draw these pictures?

@claraaldana747 3 жыл бұрын

Nice video! I will recommend it to my students as a complement to our class.

@DrTrefor 3 жыл бұрын

Cool, glad you think it will be helpful!

@suri5023 3 жыл бұрын

I was having a hard time visualizing the Plain that T and N are in. in other words, I could not understand what is the B vector. I thought the B vector WAS the plain. but now I understand that B itself is actually the normal vector of the plain that consists of T and N vectors. Thank you so much for the animation and your simple explanation.

@jaw61619 2 жыл бұрын

Excellent visual explanation ,, please do more explanation with helix

@adityaghosh766 8 ай бұрын

loved your explanation and representation sir,new subscriber and love from India

@DrTrefor 8 ай бұрын

Thanks and welcome!

@georgepp98 4 жыл бұрын

Thank you sir

@anisurrahman5498 11 ай бұрын

Thanks sir❤

@sdsa007 2 жыл бұрын

helps with the roller coaster rides at Canada’s Wonderland …and perhaps with the making of Funnel Cake which they sell at Wonderland. …or even better, Churro! Churro has a delicious texture which indicates torsion, but i believe that same delicious texture is apparent in Twister Licorices.

@ronicave8522 3 жыл бұрын

Jesus you also have videos on this, I've now been saved from my professors terrible lecture notes an non existent explanation

@DrTrefor 3 жыл бұрын

haha that sounds horrible, glad at least I could help!

@abhinayavijayan1945 3 жыл бұрын

Sir your video is really helpful to us in understanding thing in more visual way.thanku😁

@DrTrefor 3 жыл бұрын

So glad it helped!

@kck9542 3 жыл бұрын

I wish you had a lecture on elementary differential geometry.

@erickgudin 4 жыл бұрын

great!

@hayamabdelrahman3430 3 жыл бұрын

wonderful explanation

@DrTrefor 3 жыл бұрын

Glad it was helpful!

@aryanthacker 2 жыл бұрын

Hi Dr Trefor, in which video did you go over the concept discussed at 5:59 about the unit vector multiplication with its derrivative?

@sudhirtrivedi3279 3 жыл бұрын

Thx u for this ur work was superb thx

@DrTrefor 3 жыл бұрын

Glad you liked it:)

@LOG2007 4 жыл бұрын

Hi! I like the video a lot. It's very helpful. I have a question like if the dB/ds is parallel with unit vector N, so they are parallel in the same direction or opposite direction? As N always points inwards, would dB/ds also point inwards? Thank you!

@estebanlopez1701 2 жыл бұрын

underrated

@PSM1974 Жыл бұрын

Dear Dr Bazett, Thank you for the great explanation. I wanted to ask…say a particle with constant velocity is travelling in a straight line (not turning in the plane) but it is twisting on its axis (along the tangent T unit vector) how is the binormal calculated?….since if T is constant and the particle is not turning which means the normal N = 0 as well…and since the binormal is based on T and N, how is B (and hence the rate of particle twist) calculated in this case? Thanks a lot

@KOMATH 3 жыл бұрын

Great videos! Won't you mind sharing the software or applications that you're using to create these amazing graphics/animations?TIA

@DrTrefor 3 жыл бұрын

It is all done in MATLAB

@VideoFunForAll 3 жыл бұрын

So how do we generalize this into multiple (3+) dimensions?

@jamesruz6684 Жыл бұрын

i just feel each of my brain cells waking up

@continnum_radhe-radhe 2 жыл бұрын

This is the benefit of video ,...

@tolfifiz 3 жыл бұрын

hello, I found this video and I feel very thankful to you. And I have a question of what I saw in Wikipedia. I search “Frenet-Serret frame” description, and I cannot understand “suppose that the observer carries an (inertial) top (or gyroscope) with them along the curve. If the axis of the top points along the tangent to the curve, then it will be observed to rotate about its axis with angular velocity -τ relative to the observer's non-inertial coordinate system.” And, “If the top points in the direction of the binormal, then by conservation of angular momentum it must rotate in the opposite direction of the circular motion. In the limiting case when the curvature vanishes, the observer's normal precesses about the tangent vector, and similarly the top will rotate in the opposite direction of this precession.” I think it’s hard to understand because I didn’t studied calculas 3.I hope you answer me. I apologize if the nuances of my comment are little bit not polite, because I am not very familiar with the nuances of English...

@mravouvacar5302 4 жыл бұрын

thank you very much for the wonderful explanation. please are the curvature and torsion of a regular curve thesame all over the curve?

@mravouvacar5302 4 жыл бұрын

@@DrTrefor ok , does that mean the curvature and torsion are the same at all points on the curve? and what will happen to its TNB s, are they also the same at all points? thank you .

@clockedlife 4 жыл бұрын

@Trefor Bazett dr/ds is Unit Tanget Vector rather than Tangent vector. Similary dT/ds is Unit Normal Vector rather than Normal vector. It looks like complaining but being specific helps a lot of time for viewers.

@bradkevin4209 2 жыл бұрын

doctor please explain dynamic systems analysis

@n0nenone Жыл бұрын

Woah now I'm interested in a subject I did not understand jack about lol

@airsquid8532 Жыл бұрын

What would you need to do to find the normal and tangent vector if the function isn't definable in arc length?

@quantumofspace1367 4 жыл бұрын

There is a great idea! For the dark side of the Universe - suppose that it consists of short-term interactions in long-lived fractal networks, the smallest quantum operators in energy, spherical rosebuds, consisting of a large set; 1 - rolled into a sphere, 2 - half collapsed into a sphere and 3 - flat, vibrating quantum membranes relative to their working centers in the sphere