An exact time law for the teardrop-heart orbits of the μ=3 swinging Atwood machine is derived using a Poincaré time transformation, and the period is shown to be independent of launch angle in the small-radius limit.
Teardrop and heart orbits of a swinging Atwood's machine
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Motion in time of a swinging Atwood machine
An exact time law for the teardrop-heart orbits of the μ=3 swinging Atwood machine is derived using a Poincaré time transformation, and the period is shown to be independent of launch angle in the small-radius limit.