Abstract: The problem of 3-body decaying with equal mass under the condition of no initial momentum is analyzed. With the Dalitz diagram, we pressent s the energy distribution of three body and its shape in the Dalitz diagram based on the Newton＇s dynamics, extreme and non-extreme relativity theory. The shape differences and its reasons using math language and introduces its preliminary applications is also discussed

Key words: Dalitz diagram, energy distribution, extreme relativity, π^0 meson