Abstract
Classical Range Kutta (RK) methods are introduced and analyzed. And some important algorithms are outlined. The nonlinear dynamic differential equation of 2K-H planetary gear transmission, which takes into consideration of clearance, is presented in this chapter. Based on some RK algorithm, various chaotic characteristics of the numerical solution system, such as the largest Lyapunov exponent, Poincaré section, FFT spectrum, and the phase locus are collected. As the existence of clearance, the Jacobi matrix of the numerical solution system does not exist at the boundary. A new method on the Largest Lyapunov Exponent of the system is deduced based on the definition of Lyapunov Exponent. Numerical simulation results are carried out on the periodic movement, quasiperiodic movement and chaotic movement of the system.
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This work is Supported by National Key Research and Development Program of China (2017YFF0207400).
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Guo, S., Han, L. (2018). The Numerical Solutions and Their Applications in 2K-H Planetary Gear Transmission Systems. In: Stability and Control of Nonlinear Time-varying Systems. Springer, Singapore. https://doi.org/10.1007/978-981-10-8908-4_12
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DOI: https://doi.org/10.1007/978-981-10-8908-4_12
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