Talk:Elasticity

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I guess I disagree with the current definition of elasticity, because of two factors:

  1. Elasticity theory (or simply elasticity) is a branch of physics, not simply a relationship between two variables.
  2. In elasticity, the relationship between stress and strain is approximated as proportional, but is often non-linear in real life. The current definition hardwires proportionality into the definition.

I'm happy to have a list of interesting forms of elasticity in economics, but let's defer exact definitions for those articles. -- hike395 04:48 23 Jul 2003 (UTC)

OK, I made an edit, let's see how people like it. The new material seemed specific to economics, so I placed it under the subsection for economics, then restored the physics part. As I was writing, I thought of another issue, which is that, in general, a proportional effect between two variables is not called elasticity (i.e., the definition as proposed was overly general). For example, in statistics, linear regression is used to discover such proportional effects, but I've never heard that called elasticity.
So, I suspect that the definition as proposed is an economics term, so I put the prose under the economics section. Given that, we may want to consider leaving this article as a pure disambiguation page, and putting the definition into elasticity (economics). -- hike395
I do not agree with many points mentioned above. First of all, elasticity originated as, and is fundamentally a mathematical concept. It was discovered/developed by a French mathematician, a woman, if my memory serves me right. It is a measurement of the resposiveness of a dependant variable, given a change (usually a small change) in an independent variable. It is true that physicists were the first to employ the concept, but economists were not far behind. From a mathemetician's point of view, the only difference is that economists use variables such as price and quantity demanded, whereas the physicist uses variables like length and stress. The simplest form of the equation is the pecentage change in the dependant variable divided by the percentage change in the independent variable. It is sometimes refered to as the proportional change in the effected variable that results from the change in the causal variable. This is a linear approximation : a more accurate measurement is (d dep / dep) / (d in / in) . Where: d=derivitive; dep=dependant variable ; in=independent variable (or if you prefer, (d dep / d in) * ( in / dep)). These are general formulas that can be used in any discipline, anyhere that you want to measure the responsiveness of one variable to another.mydogategodshat 08:17, 7 Aug 2003 (UTC)
The problem is the current usage of elasticity in physics, which is broader than what you state, above. It's more than a linear relationship between variable, and it's even more than a single mathematical concept. It's an entire field of study (also called continuum mechanics). For example, take a look at the Table of Contents for Mathematical Foundations of Elasticity by Marsden and Hughes, starting at [1] . Note that the title of this standard (Dover) book implies that elasticity is separate from mathematics. Note that the linear form of elasticity is only derived in Chapter 4.
For more support, take a look inside of The Theory of Elasticity by Lifshitz & Landau (an old, standard text in the field) [2]. Note the first sentence of the first chapter, that states "The mechanics of solid bodies, regarded as continuous media, forms the theory of elasticity". Look at the Table of Contents in [3], where the book discussed cracks (dislocations) in Chapter 4, visco-elasticity in Chapter 5. The field really does transcend a linear relationship between two variables.

Sadly, the edits made today are not factually accurate. In physics, an inelastic collision or material is something that simply fails to obey an elasticity law. Conversely, a material can have a huge tensile strength and is said to be elastic if it obeys the linear stress-strain relationship. Under the definition of the article, this material would be called inelastic, because it deforms very little under the applied stress.

I cannot think of a way of rescuing the new material. But, I'll hold off on reverting, if someone else thinks they can fix it. -- hike395 01:04, 31 May 2004 (UTC)

Bold Change[edit]

I'm going to merge the current content here into the disambiguation page at elastic, and then I will make this page redirect there. That page has been undergoing cleanup as well. Any comments or objections should go on my talk page, please. - Corbin Be excellent 22:39, 2 July 2006 (UTC)