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References

CodePhys implements introductory physics and standard numerical methods. This page lists the primary literature behind each piece, so every integrator, law, and constant can be traced to its source — not only to the course textbook. Machine-readable BibTeX for all of these is in ../REFERENCES.bib.

Verification. Every entry with a DOI was checked against CrossRef (title, authors, volume, pages, year). Pre-DOI classics (Newton, Kepler, Euler, Kutta, Störmer) are formatted from their canonical citations. The textbook anchoring the study guide is OpenStax College Physics 2e (Urone & Hinrichs 2022).

Which source backs which part of the code

Code Concept Primary source(s)
physics/src/integrator.cpp — Explicit Euler forward Euler step Euler 1768
physics/src/integrator.cpp — Semi-implicit Euler symplectic / Störmer step Störmer 1907; Hairer, Lubich & Wanner 2003
physics/src/integrator.cpp — Velocity Verlet velocity form of Verlet Verlet 1967; Swope et al. 1982
physics/src/integrator.cpp — RK4 classical 4th-order Runge–Kutta Runge 1895; Kutta 1901
integrator theory / orders / symplecticity geometric integration Hairer, Nørsett & Wanner 1993; Hairer, Lubich & Wanner 2006
physics/src/world.cpp, app/scenes/ch03_projectile.cpp Newton's laws, kinematics, gravity Newton 1687
app/scenes/integrator_comparison.cpp, orbit test circular orbits, Kepler's third law Kepler 1609; Kepler 1619
world.cpp energy/momentum/angular-momentum readouts; tests/test_physics.cpp conservation laws Noether 1918; Goldstein et al. 2002
physics/include/physics/math/constants.hpp g, G, c, h, k_B, ε₀, … Tiesinga et al. 2021 (CODATA 2018); BIPM SI 2019
study guide course textbook OpenStax College Physics 2e 2022

Full list

Numerical integration of ODEs

  • Euler, L. (1768). Institutionum calculi integralis, Vol. 1. Imperial Academy of Sciences, St. Petersburg. — origin of the forward (explicit) Euler method.
  • Runge, C. (1895). Über die numerische Auflösung von Differentialgleichungen. Mathematische Annalen 46(2), 167–178. DOI: 10.1007/BF01446807
  • Kutta, W. (1901). Beitrag zur näherungsweisen Integration totaler Differentialgleichungen. Zeitschrift für Mathematik und Physik 46, 435–453. — with Runge, the classical RK4 method.
  • Störmer, C. (1907). Sur les trajectoires des corpuscules électrisés dans l'espace. Archives des Sciences Physiques et Naturelles 24. — origin of the Störmer (leapfrog / symplectic) method.
  • Verlet, L. (1967). Computer "experiments" on classical fluids. I. Physical Review 159(1), 98–103. DOI: 10.1103/PhysRev.159.98
  • Swope, W. C., Andersen, H. C., Berens, P. H. & Wilson, K. R. (1982). A computer simulation method … The Journal of Chemical Physics 76(1), 637–649. DOI: 10.1063/1.442716 — introduces the velocity Verlet form.
  • Hairer, E., Lubich, C. & Wanner, G. (2003). Geometric numerical integration illustrated by the Störmer–Verlet method. Acta Numerica 12, 399–450. DOI: 10.1017/S0962492902000144
  • Hairer, E., Nørsett, S. P. & Wanner, G. (1993). Solving Ordinary Differential Equations I: Nonstiff Problems (2nd ed.). Springer. DOI: 10.1007/978-3-540-78862-1
  • Hairer, E., Lubich, C. & Wanner, G. (2006). Geometric Numerical Integration (2nd ed.). Springer. DOI: 10.1007/3-540-30666-8 — symplectic integrators and energy behaviour.

Classical mechanics

  • Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica. Royal Society, London. — the three laws of motion and universal gravitation.
  • Kepler, J. (1609). Astronomia Nova. Prague. — Kepler's first and second laws.
  • Kepler, J. (1619). Harmonices Mundi. Linz. — Kepler's third law, T² ∝ a³.
  • Noether, E. (1918). Invariante Variationsprobleme. Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl., 235–257. — symmetries ⇒ conservation laws.
  • Goldstein, H., Poole, C. P. & Safko, J. L. (2002). Classical Mechanics (3rd ed.). Addison-Wesley.

Physical constants

  • Tiesinga, E., Mohr, P. J., Newell, D. B. & Taylor, B. N. (2021). CODATA recommended values of the fundamental physical constants: 2018. Reviews of Modern Physics 93(2), 025010. DOI: 10.1103/RevModPhys.93.025010
  • BIPM (2019). The International System of Units (SI) (9th ed.). — exact c, h, k_B; standard gravity g = 9.80665 m/s².

Course textbook

The links in the table jump to the matching entry; the corresponding BibTeX keys are in ../REFERENCES.bib.