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A gradient field is a vector field of the form for a scalar potential . Its curl vanishes wherever the required second derivatives commute.
For a twice continuously differentiable vector field, commuting partial derivatives and antisymmetry of the Levi-Civita symbol give
For a surface current density on an interface with unit normal , Ampère's law givesin Gaussian units, or in SI units.
The Lagrange point lies beyond the more massive primary, on the side opposite the secondary.
The longitude of ascending node is the reference-plane angle from a fixed direction to the ascending node.
Linearized vortensity is the first-order perturbation of vortensity about a background flow. For a shearing wave in a uniform Keplerian sheet, its amplitude is constant.
Surface conductivity is the conductivity of a thin layer integrated through its thickness. The sheet form of Ohm's law is .
A current sheet idealizes electric current as supported on a surface. It produces a jump in the tangential magnetic field.
During the swing of a shearing wave, the radial wavenumber passes through zero and the disturbance changes from leading to trailing before winding ever more tightly.
The Kozai–Lidov mechanism exchanges eccentricity and inclination in a hierarchical gravitational system while preserving a component of angular momentum in the quadrupole limit.
In a hierarchical orbital system, the quadrupole approximation keeps the first nontrivial term beyond the monopole in the orbit-averaged expansion in the ratio of inner to outer separation.
A secular torque is the orbit-averaged gravitational torque that changes orbital orientation or shape after fast orbital phases have been averaged out.
Resonant-argument libration is bounded oscillation of a resonant argument about a stable equilibrium value instead of circulation through all angles.
Pinned article: Introduction to the OurBigBook Project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. 
- Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact