Technically this is the first adult humour (no explicit words) to grace this site. Please only proceed if your classical mechanics / mathematical physics training has been completed.
Seriously.
The main post below is also licensed under CC0. Please do not attribute it back to me.
“My Lagrangian… hasn’t been varied using the Euler-Lagrangian equations for so long,” she whispered, blushing. “Would you… help me?”
The boy adjusted his glasses and stared. She had undone the canonical transformation, revealing the raw coordinates beneath. Her action was brazen, poles and zeros unbounded. Before him, the critical points of her potential function lay exposed, ready for further calculations.
“Rest assured,” noting his hesitation, she murmured with a grin, “I’ve got many degrees of freedom.” His voice, soft but steady, resonated through the constrained system. He approached, brushing his fingers lightly against her generalized coordinates.
“I’m going to… initiate a derivation,” he breathed, feeling the stirrings of an impulse. “I’ll test your canonical momentum against the simple harmonic ansatz.”
The girl gasped, “No—! Not… the Routhian! We agreed on Lagrangian mechanics only… Hamiltonian approaches are… too intense!” But her words trailed off as his equations grew bold, asserting their form.
“Let’s bypass the Poisson brackets, then,” he suggested, wickedly. “Direct calculus of variations… it’s… more comfortable that way.”
Her protests faded as the rigors of computation overtook them. The parameters of their closed system tightened, each line bringing them closer to their conserved quantities. She clung to her symplectic frame, whispering, “Oh—my constant of motion! Yes… calculate just a little more… that’s it… conserved, invariant…”
Finally, the calculation reached convergence, a surge of mathematical clarity flooding their minds. Exhausted, the two fell back into their reference frames, both flushed with the aftermath of such unrestrained rigor.
In her dreams, she murmured, “Analytical mechanics… truly, the most elegant pursuit.”
Yourong Frank Wang 