  We present a general formalism to write the decay amplitude for multibody
reactions with explicit separation of the rotational degrees of freedom, which
are well controlled by the spin of the decay particle, and dynamic functions on
the subchannel invariant masses, which require modeling. Using the
three-particle kinematics we demonstrate the proposed factorization, named the
Dalitz-plot decomposition. The Wigner rotations, that are subtle factors needed
by the isobar modeling in the helicity framework, are simplified with the
proposed decomposition. Consequently, we are able to provide them in an
explicit form suitable for the general case of arbitrary spins. The only
unknown model-dependent factors are the isobar lineshapes that describe the
subchannel dynamics. The advantages of the new decomposition are shown through
three examples relevant for the recent discovery of the exotic charmonium
candidate $Z_c(4430)$, the pentaquarks $P_c$, and the intriguing
$\Lambda_c^+\to pK^-\pi^+$ decay.
