Torsion: How curves twist in space, and the TNB or Frenet Frame | tnb connection | أحدث الأغاني التايلاندية

Torsion: How curves twist in space, and the TNB or Frenet Frame – معلومات الموسيقى التايلاندية

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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.

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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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Torsion: How curves twist in space, and the TNB or Frenet Frame | الصور المتعلقة بهذا الموضوع.

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

البحث المتعلق بالموضوع tnb connection.

#Torsion #curves #twist #space #TNB #Frenet #Frame.

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

tnb connection.

Example,Calculus,Multivariable,Torsion,Formula,TNB Frame,Frenet Frame,Vector,Binormal,Normal,Tangent,Serret

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29 thoughts on “Torsion: How curves twist in space, and the TNB or Frenet Frame | tnb connection | أحدث الأغاني التايلاندية”

  1. 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.

  2. Since the normal and binormal unit vectors are orthogonal and lay in the normal plane couldn’t torsion be defined as the change in the normal unit vector as well as the binormal unit vector? Like dN/ds=Tau*B

  3. At 4 min45 is it the same explanation if we take the formula of the normal vector which is N= (1/K) (dT/ds)
    and then multiply both side by kappa ? KN=(K/K)(dT/ds)
    If not i am really confuse why we are multplying the K by a normal vector>

  4. 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.

  5. 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.

  6. 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!

  7. 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 !

  8. 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 👍

  9. 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…

  10. I have a doubt. What exactly tangent vector is? In previous video u used dr/dt to calculate tangent vector. And in this video u r using dr/ds. Are both dr/dt and dr/ds same?


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