Nonrelativistic Hamiltonian in the principal central moving axes for N-particle system

This paper is concerned with derivation of a complete Hamiltonian and its r ovibronic part containing no anomalous (singular) coefficients like I-alpha /2(I-beta-I-gamma)(2) by the square components of the orbital angular momen tum for an N-particle system. The work consists of two parts. In the first part the reasons for appearance of the anomalies (in earlier papers [1,2] a s well as in more recent ones [4-9]) are analyzed and a general procedure o f removing the singularities is proposed through the correct consideration of both determination of the angular momentum and mutual displacements of t he particles. The complete description of transition from laboratory variab les to molecular ones including non-holonomic coordinates is presented. In the second part the explicit expressions of the Hamiltonians are obtained t hrough the use of tensor methods. The first of them is as follows: [GRAPHIC ] Here P-alpha, L-alpha, P-k are the components of the total momentum, the angular momentum and momenta of internal motion.