One Dimensional Conservative System with Quadratic Dissipation and Position Depending Mass

Forl a 1-D conservative system with position depending mass within dissipative medium, its effect on the body is to exert force squared of velocity, constant motion, Lagrangian, generalized linear momentum, and Hamiltonian are obtained. We apply these new results harmonic oscillator pendulum under characteristics mentioned about, obtaining their Lagrangian for case when increasing mass.