Determining the velocities and angles for a free kick problem

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dc.contributor.authorPakdemirli M.
dc.contributor.authorAksoy Y.
dc.date.accessioned2024-07-22T08:13:23Z
dc.date.available2024-07-22T08:13:23Z
dc.date.issued2015
dc.description.abstractThe free kick problem is considered for three distinct cases: (i) no air drag or lift, (ii) linear drag, and (iii) linear drag and lift. For the first case, closed form formulas are derived for the initial velocities and angles. For the second case, two coupled algebraic equations written from the trajectory equation are given and solved numerically for the initial velocities and angles. For the third case, the equations of motion are solved approximately using perturbation techniques assuming the lift coefficient to be small compared to the drag coefficient. Because the time variable cannot be eliminated between the equations, four coupled sets of algebraic equations are solved numerically for the initial velocities and angles. All three results are compared with each other and the influences of drag and lift coefficients on the velocities and angles are outlined. © 2015 Published by NRC Research Press.
dc.identifier.DOI-ID10.1139/cjp-2015-0274
dc.identifier.issn00084204
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/16330
dc.language.isoEnglish
dc.publisherCanadian Science Publishing
dc.subjectAlgebra
dc.subjectEquations of motion
dc.subjectLift
dc.subjectPerturbation techniques
dc.subjectVelocity
dc.subjectAlgebraic equations
dc.subjectCoupled set
dc.subjectDrag and lift coefficients
dc.subjectInitial velocities
dc.subjectLift coefficient
dc.subjectLinear drag
dc.subjectTime variable
dc.subjectTrajectory equation
dc.subjectDrag
dc.titleDetermining the velocities and angles for a free kick problem
dc.typeArticle

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