# Does anyone recognise this differential equation (from Gravity's Rainbow)?

In the novel Gravity's Rainbow by Thomas Pynchon, there is a chapter in which Slothrop (the main character) thinks about this equation:

$$\theta \frac{d^2\phi}{dt^2} + \delta^* \frac{d\phi}{dt} + \frac{\partial L}{\partial\alpha}(s_1-s_2)\alpha = -\frac{\partial R}{\partial\beta} s_3\beta\,.$$

It seems to be something to do with the V2 rocket, and yaw control. Does anyone recognise this equation from a book or research paper? What do the various variables stand for? He may have invented the equation, I suppose. How would one go about solving an equation like this? I find it strange that it contains both partial derivatives and total derivatives. However, there are equations in Hamiltonian mechanics like this.

Any help would be much appreciated. Thank you.

• I took the liberty of (a) including an image of the equation, and (b) specializing the title to indicate the Pynchon-source of the equation. Mar 19, 2017 at 2:53
• Googling, I stumbled on a paper by Magueijo and Smolin (2004, Classical and Quantum Gravity, Volume 21) called "Gravity's rainbow" - in context of relativity theory, they consider energy-dependent families of metrics and call these rainbow metrics.
– მამუკა ჯიბლაძე
Mar 19, 2017 at 9:46
• Maybe somebody on the Physics or Space Exploration site could shed some light. Mar 19, 2017 at 16:11
• How can I re-post this on the Space Exploration site?
– user947185
Mar 19, 2017 at 18:43
• @user947185 Flag it for moderator attention and ask them to do it.
– FFF
Mar 22, 2017 at 16:12

Schachterle, Lance, and P. K. Aravind. "The three equations in Gravity's Rainbow." Pynchon Notes 46-49 (2000): 157-170. Journal Link.

"In our view, Pynchon inscribes these equations into Gravity's Rainbow to challenge readers with yet another form of authority within the text."

Sorry—hit a pay wall...
Later: Got through the pay wall:

..........

• I myself don't accept their conclusion that this is "not a genuine mathematical expression." It seems unlikely Pynchon would concoct this without a basis in some real document. But I defer to "rocket scientists"... Mar 19, 2017 at 1:17
• There's a journal devoted entirely to the study of the works of Thomas Pynchon? And here I thought math journals were highly specialized... Mar 19, 2017 at 2:48
• @NateEldredge: "Pynchon Notes was a journal devoted to studying the works of Thomas Pynchon. Running from 1979 to 2009." 30 yrs. Mar 19, 2017 at 2:50
• Hmm. By the criterion of "two literary critics tried to pattern-match the equation against two textbooks and failed, so the equation is fake", I've a feeling that almost my entire career is fake. Mar 19, 2017 at 9:07
• @DavidRicherby, "pattern-match" may be a slightly unfair way of putting it. Note that one of the authors, P.K. Aravind is a professor of physics users.wpi.edu/~paravind (though, not, so far as I can tell, an expert on rocket science),
– j.c.
Mar 19, 2017 at 15:56

Engelhardt, N. & Engelhardt, H., (2018) “The Momentum of Pynchon's Secret Formula: Gravity’s Rainbow’s Second Equation between Archival Sources and Fiction”, Orbit: A Journal of American Literature 6(1). Journal link here

The source of the equation was found in a Control System book for the V-2 rockets. The reason the equation wasn't readily understandable was because the coefficients used were part of a larger set of equations that couldn't be known without context.

• Great! Thanks for the link. Sep 22, 2023 at 12:07
• Marvelous! I hope the OP reappears to accept this answer. Sep 22, 2023 at 15:52
• If anyone is curious, this book “History of German Guided Missiles Development” is freely available on archive.org. The pages following the image posted go into even further detail on the equation. Sep 23, 2023 at 0:11