In ballroom dancing, Elastic Time is not just stylistic — it's an energy optimization strategy. Dancers instinctively distribute Kinetic (KE) and Lost Energy \(D\) across musical time, adhering to the Principle of Least Action. Elastic time isn’t lazy timing — it’s smart physics in motion.
\[ KE = \dfrac{1}{2} m v^2\]
Related to speed and travel. Large or fast steps increase KE.
Imagine a dancer has 3 beats (e.g., in Waltz) over T_total = 2s.
| Beat | Movement | Duration (s) | KE ↑/↓ |
|---|---|---|---|
| 1 | Drive / Launch | 0.6 | ↑↑ |
| 2 | Shape / Rise | 0.8 | ↓ |
| 3 | Recovery / Lower | 0.6 | — |
Instead of dividing time equally (0.667s/beat), the dancer stretches Beat 2 to shape and rise. To maintain the total 2s, Beats 1 and 3 compress slightly, increasing their KE demands.
This redistribution respects physics and music.
The Principle of Least Action from physics:
A system moves between two states in the way that minimizes the total "action" (integral of Lagrangian = KE − LE over time).
Where LE represents the losses in the system from fighting gravity, friction, imbalances in the connection, etc.
In plain English:
Dancers seek movement pathways that feel smooth, require minimal effort, and look natural — even if that means bending the beat.
Elastic time is Least Action at work — unconsciously.
Given that the 'least action' term crops up so often and is so important you might want to take a closer look: The Lagrangian In Dance (because 'least action' crops up a lot)
When a dancer extends a shaping moment by stretching Beat 2:
This isn't "sloppy timing" — it's a form of Newtonian artistry.
Music isn’t rigid. It breathes.
Total energy expenditure across a bar is minimized if:
\[ \text{Total Action} = \int_{t_0}^{t_f} (KE - D)\, dt \quad \text{is minimized}\]
Note that this is a simplified equation as \(D\) would be included using the Rayleigh dissipation \(D\).
Dancers naturally solve this equation — without knowing it.
Elastic Time is not a cheat. It’s an optimization.
Dancers don’t just “stay on time.”
They inhabit time.
They sculpt it with energy.
Isaac Newton - Laws of Motion, which define the relationships between force, mass, and acceleration - the backbone of dance biomechanics.
Pierre-Louis Moreau de Maupertuis - Principle of Least Action. Maupertuis proposed that nature operates by minimizing action, laying groundwork for modern physics and biomechanics.
Leonhard Euler - Expanded on Maupertuis’ ideas and gave mathematical form to the Principle of Least Action. His work underpins the Euler-Lagrange equations.
Joseph-Louis Lagrange - Developed the Lagrangian Mechanics formalism, which allows us to model motion in terms of energy rather than force. Vital for understanding how dancers conserve or redistribute energy.
William Rowan Hamilton - Introduced Hamiltonian Mechanics, which provides an alternative formulation and links energy conservation with system evolution over time.
Émilie du Châtelet - Translated and extended Newton’s work, particularly his Principia, and was one of the first to clarify that kinetic energy was proportional to the square of velocity (i.e., \(v^2\)). Hugely underrated.
We stand on the shoulders of giants. (And some of them wore wigs).