Sundman theorem revisited

In this paper, we revisit Sundman’s Theorem on the three-body problem. We provide a simple example demonstrating that the requirement on the total angular momentum L (bounded away from zero) can be relaxed for a particular set of initial conditions, allowing double shocks. We present an explicit solution for the exact triple-collision scenario through a Sundman-like formal regularization. •Implicit Exact Solution for a triple shock.•Explicit Exact regularized solution for a triple shock.•A simple example where a Sundman series exists with zero total angular momentum.•A relation between the pseudo-time and the total mass for a triple shock.