# Talk:Kinematics

### Trace

This lesson uses the trace ${\displaystyle {\text{Tr}}}$. This doesn't seemed to be defined in the lesson or math review. For the sake of clarity (it took me a minute to figure out what it was) and rigor, I think it should be defined. I'm not entirely comfortable with my terminology, so I am not adding a definition myself.

Papna 02:21, 24 October 2007 (UTC)

I have added a crude definition of the trace. Please add a basis independent definition if you can. Banerjee 04:54, 28 November 2007 (UTC)

### Displacement

displacement=distance moved from starting location to ending location when a force is applied to a solid material Mirwin 05:12, 27 November 2007 (UTC)

strains=stretch in material to allow displacement experience from that force Mirwin 05:12, 27 November 2007 (UTC)

The displacement is defined independent of what causes it. These definitions are very basic and should be part of the Strength of Materials course. Banerjee 04:54, 28 November 2007 (UTC)

### Infinitesimal

infinitesimal means ... what? I think the use of the term implies we think the axioms and postulate upon which calculus is based are operative ... in other words if the increment size is small enough errors in answers of the summing functions|operators? we use will fade out and as a practical matter be close enough to zero that our solution while not perfect is witin specified performance parameters and constraint and tolerances can somebody paraphrase and agree or disgree to build my confidence thus motivated moving on or making me nervous enough to spend some more time reviewing before depending on my equations and calculated answers. Thanks! Mirwin 05:12, 27 November 2007 (UTC)

The word infinitesimal has a very specific meaning in the context of linear elasticity (and strength of materials, where it is first presented to the student). For our purposes, it means strains that are so small that the stress-strain relations can be considered linear. Banerjee 04:54, 28 November 2007 (UTC)

### Finite theory

finite implies in this use not infinite. In other words we can state a definate upper limit or bound. The math (and memory size requirements in computer processor) does not go to infinity when operating with finite numbers and elements? Can say yes no maybe? If this no otherwise correct? Mirwin 05:12, 27 November 2007 (UTC)

The word "finite" in the context of elasticity (and applied mechanics in general) has a very specific meaning. It indicates that strains are not infinitesimal. Note that infinitesimal does not mean zero. Banerjee 04:54, 28 November 2007 (UTC)

### Displacement (definition)

<question>So if one assigns a coordinate system to the space volume occupied by a solid object and then provide basis vectors of coordinate system allocated to the object of interest there should be a linear transformation (a matrix one can multiply by the first matrice of designated points to arrive at the location of each individual point inside the object after the object has been deformed (rather than merely displaced)from original rest state by an applied load</question> Mirwin 05:20, 27 November 2007 (UTC)

Yes. That's correct. The object that has that property is called the "deformation gradient" which is a two point tensor. It doesn't matter whether the object has been deformed or merely "displaced". As long as there are two configurations and you can create a map you will have a deformation gradient which may or may not be the identity. Banerjee 05:00, 28 November 2007 (UTC)

## Finite rotational tensor?

Is there a finite-strain equivalent of the infinitesimal rotation tensor? In the infinitesimal case there is a nice decomposition of the displacement gradient into symmetric (${\displaystyle \epsilon }$) and skew-symmetric (W) components; in the finite-strain case, E is again symmetric, but it is not so obvious to me that there is a sensible skew-symmetric counterpart. Thanks, Ged.R 09:30, 11 November 2008 (UTC)