PARTIENDO DEL HECHO DE QUE PARA UN SISTEMA MECÁNICO AUTÓNOMO ARBITRARIO CUALQUIER CONSTANTE DE MOVIMIENTO PUEDE USARSE COMO HAMILTONIANA, SE DEDUCE LA EXPRESIÓN PARA LAS LAGRANGIANAS DE UN SISTEMA MECÁNICO UNIDIMENSIONAL PREVIAMENTE HALLADA POR OTROS AUTORES.AbstractSTARTING FROM THE FACT THAT FOR AN ARBITRARY AUTONOMOUS MECHANICAL SYSTEM ANY CONSTANT OF MOTION CAN BE USED AS HAMILTONIAN, THE EXPRESSION FOR THE LAGRANGIANS OF A ONE-DIMENSIONAL MECHANICAL SYSTEM PREVIOUSLY FOUND BY OTHER AUTHORS IS DERIVED.STARTING FROM THE FACT THAT FOR AN ARBITRARY AUTONOMOUS MECHANICAL SYSTEM ANY CONSTANT OF MOTION CAN BE USED AS HAMILTONIAN, THE EXPRESSION FOR THE LAGRANGIANS OF A ONE-DIMENSIONAL MECHANICAL SYSTEM PREVIOUSLY FOUND BY OTHER AUTHORS IS DERIVED.