This paper is devoted to a systematic study of quadratic systems of second-order ordinary differential equations which are defined in commutative algebras. Conserved quantities are found and several examples defined in Jordan and Nahm algebras are analyzed. Hamiltonian and gradient systems are considered.
"On second-order quadratic systems and algebras." Differential Integral Equations 24 (9/10) 877 - 894, September/October 2011.