daviddoji/CalculusWithJuliaNotes.jl
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

WIP

Browse Source
This commit is contained in:
jverzani
2025-08-29 15:33:24 -04:00
parent 7c869a83ce
commit c044529cba
5 changed files with 133 additions and 5 deletions
Download Patch File Download Diff File Expand all files Collapse all files

3
quarto/differentiable_vector_calculus/vector_valued_functions.qmd
View File

@@ -1038,8 +1038,7 @@ $$
---
Kepler's second law can also be derived from vector calculus. This derivation follows that given at [MIT OpenCourseWare](https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-c-parametric-equations-for-curves/session-21-keplers-second-law/MIT18_02SC_MNotes_k.pdf) and [OpenCourseWare](https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/index.htm).
Kepler's second law can also be derived from vector calculus. This derivation follows that given at MIT OpenCourseWare (link defunct); a succinct approach is given by [Strang](https://ocw.mit.edu/courses/res-18-001-calculus-fall-2023/mitres_18_001_f17_ch12.pdf).
The second law states that the area being swept out during a time duration only depends on the duration of time, not the time. Let $\Delta t$ be this duration. Then if $\vec{x}(t)$ is the position vector, as above, we have the area swept out between $t$ and $t + \Delta t$ is visualized along the lines of: