Abstract
In this article, we present a novel survey of known qualitative features of the isosceles trapezoidal four-body problem, that has three degrees of freedom, as well as its two subsystems with two degrees of freedom, namely, the symmetric collinear four-body problem and the rectangular four-body problem. We use the configurations space to display the “full picture” that allows us to visualize all admissible configurations on the reduced space, homeomorphic to a three-sphere, called the shape sphere.
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