Abstract.This paper presents a modeling and simulation method for analyzing position, velocity, and acceleration of riding objects on recreational waterslides represented in computer-aided design (CAD) environment. Mathematical representations of a number of common flume sections are first created in parametric surfaces. A set of coupled differential equations based on Lagrange's equation of motion that describe the motion of the riding object are derived, in which friction forces are included. These second order differential equations are then solved using Mathematica. Initial position and velocity are specified for the entire waterslide, which is composed of basic flume sections. A different set of differential equations are solved for each section. The position and velocity of the riding object at the entrance of the following section are obtained from those at the exit of the previous neighboring section. A real-world waterslide configuration is presented to demonstrate the feasibility of the modeling and simulation method. The major contribution of the paper is extending waterslide simulation to true CAD-based flume sections, and bringing friction forces into the formulations that make the simulations more realistic.

Received: August 17, 2007

AMS Subject Classification: 70A02

Key Words and Phrases: computer-aided design, differential equations, waterslides

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 3