Torsion Definition and 217 Threads

why torsion free metric compatible connection ? Why in conventional GR we choose a torsion free, metric compatible connection? Can that be derived from somewhere like physical principles/postulates or it's just a the simplest convenient choice (many terms drop from equations) that produces...

Homework Statement Does a torsion module M imply M is cyclic? Or does it imply M is finitely generated? I think cyclic implies torsion module. What about the reverse? The Attempt at a Solution I think there is a connection but don't see it.

Can someone pleas explain to me the geometric interpretation of Torsion? Why it is true is more important. Lol i said manifolds instead of torsion!

Homework Statement Suppose \alpha is a regular curve in \mathbb{R}^3 with arc-length parametrization such that the torsion \tau(s)\neq 0, and suppose that there is a vector Y\in \mathbb{R}^3 such that <\alpha',Y>=A for some constant A. Show that \frac{k(s)}{\tau(s)}=B for some constant B...

Hi, I've been studying extensions of general relativity with the torsion tensor and I have been wondering about the following fact: what is the physical meaning of the three indices of this tensor? That is, do these three indices represent some directions in space? (For example, the translation...

Homework Statement Find the unit speed curve alpha(s) with k(s)=1/(1+s^2) and tau defined as 0. Homework Equations Use the Frenet-Serret equations K(s) is the curvature and tau is the torsion T= tangent vector field (1st derivative of alpha vector) N= Normal vector field (T'/k(s))...

Here's something for the phone book's fans to chew on: Surprisingly, on page #1278, in the index entry "Torsion", the 3 authors claim that "(torsion) not present in affine connection if equivalence principle is valid" and hint further to page #250 where they don't debate on it. However...

Okay, so I was asked to find all the things listed in the topic title given the equation: r(t)=(cos^{3}t)\vec{i} + (sin^{3}t)\vec{j} Now this is a lot of work, especially when it comes to finding the torsion \tau = - \frac{d \vec{B}}{ds} \cdot \vec{N} a total of four derivitives. Maybe I am...

I am trying to calculate the diameter of a drive shaft. I would have thought that all I would need in order to determine the diameter of a shaft (concerning torsion) would be how much torque is going to be applied to the shaft and the shear modulus rating of the drive shaft material...

what formula should i use to calculate the shaft diameter according to the load due to bending and torsion??

Hi there, can anyone just help me in finding articles, notes, theories about Hardness tests(Brinnel, Vickers, Rockwell) and Torsion test...please

I've always wondered, and I can't seem to find out...

Is anyone familiar with the derivation for this formula for torsion. \tau = \frac {\left( \begin{array}{ccc} \dot{x} & \ddot{x} & \dddot{x}\\\dot{y}& \ddot{y}& \ddot{y} \\\dot{z} & \ddot{z} & \dddot{z}\end{array} \right)} {|v \times a|^2} I know of expressing torsion as [tex] \tau =...

Hi guys, Just a quick question. I have been attempting some problems to do with torsion. Most are pretty standard, you know, find the torque, angular rotation etc. However I am stuck on this one. I have calculated the torque and rotation for a shaft that's at its proportional limit...

I'm looking either for online resources or reference to a good book. I've been trying to help someone with a homework problem in a course entitled, Elements of Mechanical Design which uses Mechanical Design of Machine Elements and Machines by Jack A. Collins. The book sucks. The system...

Could someone please point me in the right direction for finding formulas dealing with torsion springs and also understanding more about how they work? Thanks Carla

A uniform meter stick is hung at its center from a thin wire. It is twisted and oscillates with a period of 5 s. The meter stick is then sawed off to a length of 0.76 m, rebalanced at its center, and set into oscillation. ****************** With what period does it now oscillate? Ok, I...