User:Raazer

This user page is a scrapbook of stuff, and not a description of me

Working with energy dissipation mechanisms is difficult because the forces produced by the rubber bands is a function of stretch distance. In regards to our impact design, the force would vary over the time of impact. The easiest way to describe a varying force in the case of an impact is using the principle of impulse and momentum. The equation:

$\int _{t_{1}}^{t_{2}}\sum F(t)\,dt=mv_{2}-mv_{1}$

${{t_{2}}-{t_{1}}}F_{av}=mv_{2}-mv_{1}$

Using LaTeX markup

Wikipedia allows editors to typeset mathematical formulas in (a subset of) LaTeX markup (see also TeX); the formulas are normally translated into PNG images, but may be rendered as HTML or MathML, depending on user preferences. For the mechanics of this, see meta:Help:Formula.

The LaTeX formulas can be displayed in-line (like this: $\mathbf {x} \in \mathbb {R} ^{2}$), as well as on their own line:

$\int _{0}^{\infty }e^{-x^{2}}\,dx$

$u(t)=K_{P}e(t)+K_{D}{\frac {d}{dt}}e(t)$

Having LaTeX-based formulas in-line which render as PNG under the default user settings, as above, is generally discouraged, for the following reasons.

• The font size is somewhat larger than normal, making text containing in-line formulas hard to read.
• The download speed of a page is negatively affected if it contains many images.
• HTML (as described below) is adequate for most simple in-line formulas and better for text-only browsers.

When displaying formulas on their own line, one should indent the line with one or more colons (:); the above was typeset as

:<math>\int_0^\infty e^{-x^2}\,dx</math>

If you find an article which indents lines with spaces in order to achieve some formula layout effect, you should convert the formula to LaTeX markup.

If you plan on editing LaTeX formulas, it is helpful if you leave your preference settings (link in the upper right corner of this page, underneath your user name) in the "rendering math" section at the default "HTML if very simple or else PNG"; that way, you'll see the page like most users will see it.

Very simple formulas

If you enter a very simple formula using the math notations like <math>L^p</math> this will (in the default used by most users) not be displayed using a PNG image but using HTML, like this: L^p. This is different from typesetting it as ''L''<sup>''p''</sup>. Compare:

LaTeX rendered as HTML: L^p

HTML: L^p

Either form is acceptable, but do not change one form to the other in other people's writing. They are likely to get annoyed since this seems to be a highly emotional issue. Changing to make an entire article consistent is acceptable.

However, still try to avoid in-line PNG images. Even if you use <math>L^p</math> throughout the article, use ''L''<sup>&infin;</sup> to get L^∞ rather than the LaTeX-based $L^{\infty }$, which doesn't always look good.

If you want to force an image output for a simple formula, put a \, (one quarter space in LaTeX) at the end of the formula, or \!\, (one negative quarter space and one quarter space).