Strong Inequality Hydrodynamics: Flat Cylinder in Water

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The discussion focuses on the implementation of a hydrodynamic simulation involving a flat cylinder in water, specifically within the context of the Shadowfang Keep instance in a gaming environment. It includes references to various open-source projects and licenses, emphasizing the program's free software status under the GNU General Public License. The code snippet outlines the structure for managing encounters within the instance, detailing four specific encounters with named characters. The script is designed to enhance gameplay by providing a structured approach to instance management. Overall, the conversation highlights technical aspects of game development related to hydrodynamics and instance scripting.
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So, there's a flat cylinder with radius R and Height H fully submerged in water rn. it's denser than water and its distance from its base to the bottom of the tank is h. I gotta calculate the time taken to sink to the bottom, and gotta ignore viscosity so no drag force or turbulence. BUT, what's bugging me is this inequality-
Relevant Equations
10rho_cylinder h<< rho_water R
20221128_111257.jpg
 
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/* * Copyright (C) 2011-2012 DarkCore <http://www.darkpeninsula.eu/> * Copyright (C) 2011-2012 Project SkyFire <http://www.projectskyfire.org/> * Copyright (C) 2008-2012 TrinityCore <http://www.trinitycore.org/> * Copyright (C) 2005-2012 MaNGOS <http://getmangos.com/> * This program is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the * Free Software Foundation; either version 3 of the License, or (at your * option) any later version. * * This program is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for * more details. * * You should have received a copy of the GNU General Public License along * with this program. If not, see <http://www.gnu.org/licenses/>. *//* ScriptDataSDName: Instance_Shadowfang_KeepSD%Complete: 90SDComment:SDCategory: Shadowfang KeepEndScriptData */#include "ScriptPCH.h"#include "shadowfang_keep.h"#define MAX_ENCOUNTER 4/* Shadowfang Keep encounters:0 - Commander Springvale1 - Baron Ashbury2 - Baron Silverlaine3 - Commander Grimburg*/class instance_shadowfang_keep : public InstanceMapScript{public: instance_shadowfang_keep() : InstanceMapScript("instance_shadowfang_keep", 33) { } InstanceScript* GetInstanceScript(InstanceMap* pMap) const { return new instance_shadowfang_keep_InstanceMapScript(pMap); } struct instance_shadowfang_keep_InstanceMapScript : public InstanceScript { instance_shadowfang_keep_InstanceMapScript(Map* pMap) : InstanceScript(p
 
I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW

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