Nonlinear oscillation modes of spatial double pendulum

Abstract The article studies nonlinear oscillations of a double mathematical pendulum which axes of the cylindrical joints are not collinear to each other and constitute an acute angle between themselves. Nonlinear oscillation modes of the system are constructed and analyzed in the first approximation using asymptotic methods. A quantitative verification of the obtained results is carried out by considering particular cases of a plane and orthogonal double pendulum and monitoring the energy integral in the appropriate approximation. The constructed analytical solutions are accompanied by graphic illustrations that clarify the essence of the solution.