On the hydrodynamic vertical impact problem: an analytical mechanics approach

Casetta, Leonardo; Pesce, Celso Pupo; Santos, Flávia Monique

doi:10.1007/bf03449256

Cited by 2 publications

(4 citation statements)

References 12 publications

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“…On the other hand, if this dependence is explicitly taken into account, additional non-conservative generalized force terms come into play, modifying the resulting expressions, as in Eqs. (17) and (23).…”

Section: Discussionmentioning

confidence: 99%

“…(21)-(23), we arrive at: This is another form of expressing Lagrange's equations for discrete systems of variable mass, which is equivalent to the form expressed by Eq. (23). This form is somehow simpler than that of Eq.…”

Section: Appendix: Lagrange's Equations For Discrete Systems With Varmentioning

confidence: 96%

“…This is the same extended Lagrange's equation derived by Pesce [1], from the principle of virtual work applied to d'Alembert's principle. Besides consistent, such an equation has proved useful to explaining a number of apparent paradoxes: classic ones related to recurrent controversial discussions regarding Cayley's falling chain problemsdefinitely asserting Cayley's solution; analogous ones, concerning the proper equation of motion of vertically collapsing buildings, [20][21][22]; or even non-usual ones, as those related to the proper equation governing the impact of solid bodies against a liquid surface, [1,23]. An alternative form of Lagrange's equations for systems of variable mass, not seen in any previous work, is presented in the Appendix, as an additional result of the present discussion.…”

Section: An Application Example: Cayley's Falling Chain Problemmentioning

confidence: 99%

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On Hamilton’s principle for discrete systems of variable mass and the corresponding Lagrange’s equations

Guttner

Pesce

2016

J Braz. Soc. Mech. Sci. Eng.

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proper formalism for variable-mass systems started with the pioneer works of Buquoy (see [4]), Cayley [5], and Meshchersky (see [6]) in the nineteenth century, being still a current research field; see, e.g., [7-13]. Indeed, the interest upon this theme has regained strength, as testimonies the advanced course organized in 2012 by CISM-the International Center for Mechanical Sciences, followed by the upcoming text edited by Hans Irschik and Alexander Belyaev, [14]. Within Analytical Mechanics, Lagrange's equations have to be properly reinterpreted for systems with variable masses, especially when dependent explicitly on position or velocity. In fact, in this general case, their proper form includes extra non-conservative generalized force terms. Cveticanin [8] derived the extended Lagrange's equations for discrete systems of variable mass, considering that the masses of the particles are explicitly dependent on time and generalized coordinates. Pesce [1], departing from d'Alembert's principle and following the classical Lagrangian approach, using the principle of virtual work, extended that deduction to the case where mass is also explicitly dependent on generalized velocities. Concerning continuous systems, Casetta and Pesce [12] obtained the generalized Hamilton's principle for a nonmaterial (control) volume, which was showed to be consistent with Lagrange's equation for a non-material volume previously derived by Irschik and Holl [10]. Pesce and Casetta [19] proposed a form of Hamilton's principle for discrete systems of variable mass and showed this form to be consistent with the extended Lagrange's equations derived by Pesce [1]. Employing an alternative mathematical approach, Casetta and Pesce [12] addressed the inverse problem of Lagrangian mechanics for Meshchersky's equation, by finding a Lagrangian that, when inserted into the stationary action principle, yields the equation of motion for a system of variable mass. In this study, the classical deduction of Hamilton's principle, as found in, e.g., Pars [15] or Meirovitch [16],

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Section: Discussionmentioning

confidence: 99%

Section: Appendix: Lagrange's Equations For Discrete Systems With Varmentioning

confidence: 96%

Section: An Application Example: Cayley's Falling Chain Problemmentioning

confidence: 99%

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On Hamilton’s principle for discrete systems of variable mass and the corresponding Lagrange’s equations

Guttner

Pesce

2016

J Braz. Soc. Mech. Sci. Eng.

Self Cite

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“…Another method is based on energy theory, which was derived by Wu [35]. It has more physical significance and is widely used [36][37][38]. The relationship between slamming force and added mass is…”

Section: Water Entrymentioning

confidence: 99%

Computational Model for Simulation of Lifeboat Free-Fall during Its Launching from Ship in Rough Seas

Qiu

Ren

2020

JMSE

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In order to improve the accuracy of the freefall of lifeboat motion simulation in a ship life-saving simulation training system, a mathematical model using the strip theory and Kane’s method is established for the freefall of the lifeboat into the water from a ship. With the boat moving on a skid, the model of the ship’s maneuvering mathematical group (MMG) is used to model the motion of the ship in the waves. Based on the formula of elasticity and friction theory, the forces of the skid acting on the boat are calculated. When the boat enters the water, according to the analytical solution theory of slamming, the slamming force of water entry is solved. The simulation experiments are carried out by the established model. The results of the numerical simulation are compared with the calculation results of the hydrodynamics software Star CCM+ at water entry under initial condition A in the paper. The position and velocity of the center of gravity of the boat, the angle, and velocity and acceleration of pitch calculated by the two methods are in good agreement. There is a little difference between the values of translation acceleration calculated by the two methods, which is acceptable. This shows that our numerical algorithm has good accuracy. A qualitative analysis is performed to find the safe point of water entry under the condition of different wave heights and two situations of a ship encountering waves. Finally, the model is applied to the ship life-saving training system. The model can meet the system requirements and improve the accuracy of the simulation.

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On the hydrodynamic vertical impact problem: an analytical mechanics approach

Cited by 2 publications

References 12 publications

On Hamilton’s principle for discrete systems of variable mass and the corresponding Lagrange’s equations

On Hamilton’s principle for discrete systems of variable mass and the corresponding Lagrange’s equations

Computational Model for Simulation of Lifeboat Free-Fall during Its Launching from Ship in Rough Seas

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