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ERIC Number: EJ896414
Record Type: Journal
Publication Date: 2010-Jul
Pages: 14
Abstractor: As Provided
Reference Count: 9
ISSN: ISSN-0143-0807
Roller Coasters without Differential Equations--A Newtonian Approach to Constrained Motion
Muller, Rainer
European Journal of Physics, v31 n4 p835-848 Jul 2010
Within the context of Newton's equation, we present a simple approach to the constrained motion of a body forced to move along a specified trajectory. Because the formalism uses a local frame of reference, it is simpler than other methods, making more complicated geometries accessible. No Lagrangian multipliers are necessary to determine the constraining forces. Although the method is able to deal with friction, it becomes particularly simple for conservative systems. We give an analytic expression for the constraining force for any two-dimensional frictionless trajectory that can be written in the form y = f(x). The approach is illustrated with examples from roller coaster physics, e.g. the camelback or the clothoid loop. It is possible to find analytic expressions for the constraining force in both cases. (Contains 13 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A