謝辞
以下は、Elara プロジェクトが参照した資料の一覧です。
- http://www.stat.ucla.edu/~ywu/linear.pdf
- https://www.lehman.edu/faculty/dgaranin/Mathematical_Physics/Mathematical_physics-13-Partial_differential_equations.pdf
- http://scipp.ucsc.edu/~haber/ph5B/sho09.pdf
- https://web.math.ucsb.edu/~moore/pde.pdf
- https://www.math.usm.edu/lambers/mat417/spr14/lecture14.pdf
- https://www.math.hmc.edu/~ajb/PCMI/lecture7.pdf
- https://www.seas.upenn.edu/~amyers/NaturalUnits.pdf
- http://www.roma1.infn.it/teongrav/leonardo/bh/bhcap4.pdf
- http://www.roma1.infn.it/teongrav/leonardo/bh/bhcap3.pdf
- https://www.roma1.infn.it/teongrav/onde19_20/geodetiche_Kerr.pdf
- https://math.uchicago.edu/~may/REU2012/REUPapers/Presman.pdf
- https://www.ita.uni-heidelberg.de/~dullemond/lectures/tensor/tensor.pdf
- https://www.etsu.edu/cas/math/documents/theses/simpson-thesis.pdf
- https://prasadsachchidanand.github.io/assets/attachments/Geodesic_Equation_with_Euler_Lagrange_Equation.pdf
- https://web.mit.edu/8.962/www/probsets/ps02-grs18.pdf
- https://web.physics.ucsb.edu/~gravitybook/websups/Ch8.pdf
- http://people.uncw.edu/hermanr/GR/geodesic.pdf
- http://web.mit.edu/edbert/GR/gr1.pdf
- https://www.athabascau.ca/math-site/documents/math-site-mathematics-of-tensors-introduction.pdf
- https://www.numerade.com/ask/question/proof-of-euler-formula-the-standard-proof-for-euler-formnula-cos-isin-0-uses-the-taylor-series-of-e-cos-and-sin-_-this-problem-walks-you-through-an-alternate-proof-using-ideas-from-different-52748/
- http://people.uncw.edu/hermanr/GR/geodesic.pdf
- https://www1.maths.leeds.ac.uk/~serguei/teaching/gr.pdf
- Einstein summation convention: https://www.youtube.com/watch?v=CLrTj7D2fLM
- https://planetmath.org/derivationofwaveequationfrommaxwellsequations
- https://complex-analysis.com/
- https://phys.libretexts.org/Courses/Skidmore_College/Introduction_to_General_Relativity/03%3A_Schwarzschild_Orbits/3.02%3A_Constants_of_Motion
- https://www.roma1.infn.it/teongrav/onde19_20/kerr.pdf
- https://physics.stackexchange.com/questions/316136/derivation-for-alcubierre-drive
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electro-Optics/Direct_Energy_(Mitofsky)/11%3A_Calculus_of_Variations/11.03%3A_Derivation_of_the_Euler-Lagrange_Equation
- https://youtu.be/MzRCDLre1b4
- https://youtu.be/Wb7c60GLXPk
- https://ekamperi.github.io/mathematics/2019/10/29/riemann-curvature-tensor.html
- http://einsteinrelativelyeasy.com/index.php/general-relativity/60-covariant-differentiation-exercise-2-calculation-for-the-euclidean-metric-tensor
- https://math.stackexchange.com/questions/890552/nth-derivative-of-determinant-wrt-matrix
- https://jfuchs.hotell.kau.se/kurs/amek/prst/17_wfee.pdf
- https://www.quora.com/Can-you-derive-the-Einstein-Field-equations-by-using-the-Euler-Lagrange-equations
- https://physics.stackexchange.com/questions/363602/calculating-the-determinant-of-a-metric-tensor
- https://physics.stackexchange.com/questions/211930/how-can-we-recover-the-newtonian-gravitational-potential-from-the-metric-of-gene
- https://www1.maths.leeds.ac.uk/~kersale/Teach/M3414/Notes/m3414_1.pdf
- https://physics.stackexchange.com/questions/153302/modeling-external-forces-in-lagrangian-dynamics
- https://physics.stackexchange.com/questions/271031/why-is-the-potential-energy-equal-to-the-negative-integral-of-a-force
- https://physics.stackexchange.com/questions/462213/how-to-calculate-initial-conditions-to-integrate-a-null-geodesic