The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamical models and then applied for ship roll dynamics under random impulsive white noise excitation.

Cottone, G., Di Paola, M., Ibrahim, R., Pirrotta, A., Santoro, R. (2009). Ship roll motion under stochastic agencies using path integral method. In Vibro-Impact Dynamics of Ocean Systems and Related Problems (pp. 29-40). Berlin : Springer [10.1007/978-3-642-00629-6_4].

### Ship roll motion under stochastic agencies using path integral method

#### Abstract

The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamical models and then applied for ship roll dynamics under random impulsive white noise excitation.
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2009
Cottone, G., Di Paola, M., Ibrahim, R., Pirrotta, A., Santoro, R. (2009). Ship roll motion under stochastic agencies using path integral method. In Vibro-Impact Dynamics of Ocean Systems and Related Problems (pp. 29-40). Berlin : Springer [10.1007/978-3-642-00629-6_4].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10447/41537`
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