Tractrix with inertia. (10th June 2021)

• Record Type: Journal Article
• Authors: Denny, Mark
• Is Part Of: European journal of physics. Volume 42:Number 4(2021)
• Publication Date: 2021-06-10
• Subjects: tractrix -- pursuit curve -- mechanical curve -- inertia -- Euler Lagrange -- Coulomb friction; Physics -- Periodicals; Physics -- Study and teaching (Higher) -- Europe -- Periodicals; 530
• DOI: 10.1088/1361-6404/ac0102
• Languages: English
• ISSNs: 0143-0807

Abstract

Abstract: The tractrix is a special type of pursuit trajectory with unphysical properties chosen for its mathematical interest. The trajectory can be made more physically reasonable by including the effects of inertia and of friction. Here the 'inertial tractrix' locus is derived analytically using the Euler–Lagrange approach and is found, in the absence of friction, to be a cycloid. The effects of friction are determined by numerical calculation, which show that the tractrix and cycloid loci are limiting cases as the friction coefficient becomes large and small, respectively. The analysis is extended to include variable driving velocity.