# An efficient Newton method for general motorcycle kinematics

A. Saccon, J. Hauser

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

6 Citaties (Scopus)

### Uittreksel

This paper presents a detailed study of the kinematics of single-track\nvehicles, with a special emphasis on motorcycles. We consider a general\nclass of tyre profiles as well as general vehicle geometry. We show\nthat the kinematic problem may be reduced to the problem of finding\nthe zero of a (single) nonlinear equation in the pitch angle which\nmay then be solved using a safeguarded Newton method, providing rapid\nconvergence. Special care, enabled by the systematic use of rotation\nmatrices, is taken to understand the range of pitch angles for which\nall quantities in the equation are well defined. The paper provides\na fast and numerically reliable algorithm that can be used within\nanalysis tools such as those involving numerical integration of system\ndynamics.
Originele taal-2 Engels 221-241 21 Vehicle System Dynamics 47 2 https://doi.org/10.1080/00423110801966108 Gepubliceerd - feb 2009

### Vingerafdruk

Motorcycles
Newton-Raphson method
Kinematics
Nonlinear equations
Tires
Geometry

### Citeer dit

@article{d551e4aa5c4b4edcbdde672dd7cd5185,
title = "An efficient Newton method for general motorcycle kinematics",
abstract = "This paper presents a detailed study of the kinematics of single-track\nvehicles, with a special emphasis on motorcycles. We consider a general\nclass of tyre profiles as well as general vehicle geometry. We show\nthat the kinematic problem may be reduced to the problem of finding\nthe zero of a (single) nonlinear equation in the pitch angle which\nmay then be solved using a safeguarded Newton method, providing rapid\nconvergence. Special care, enabled by the systematic use of rotation\nmatrices, is taken to understand the range of pitch angles for which\nall quantities in the equation are well defined. The paper provides\na fast and numerically reliable algorithm that can be used within\nanalysis tools such as those involving numerical integration of system\ndynamics.",
keywords = "Newton method, bicycle, kinematics, motorcycle, single-track vehicles",
author = "A. Saccon and J. Hauser",
year = "2009",
month = "2",
doi = "10.1080/00423110801966108",
language = "English",
volume = "47",
pages = "221--241",
journal = "Vehicle System Dynamics",
issn = "0042-3114",
publisher = "Taylor and Francis Ltd.",
number = "2",

}

In: Vehicle System Dynamics, Vol. 47, Nr. 2, 02.2009, blz. 221-241.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

T1 - An efficient Newton method for general motorcycle kinematics

AU - Saccon, A.

AU - Hauser, J.

PY - 2009/2

Y1 - 2009/2

N2 - This paper presents a detailed study of the kinematics of single-track\nvehicles, with a special emphasis on motorcycles. We consider a general\nclass of tyre profiles as well as general vehicle geometry. We show\nthat the kinematic problem may be reduced to the problem of finding\nthe zero of a (single) nonlinear equation in the pitch angle which\nmay then be solved using a safeguarded Newton method, providing rapid\nconvergence. Special care, enabled by the systematic use of rotation\nmatrices, is taken to understand the range of pitch angles for which\nall quantities in the equation are well defined. The paper provides\na fast and numerically reliable algorithm that can be used within\nanalysis tools such as those involving numerical integration of system\ndynamics.

AB - This paper presents a detailed study of the kinematics of single-track\nvehicles, with a special emphasis on motorcycles. We consider a general\nclass of tyre profiles as well as general vehicle geometry. We show\nthat the kinematic problem may be reduced to the problem of finding\nthe zero of a (single) nonlinear equation in the pitch angle which\nmay then be solved using a safeguarded Newton method, providing rapid\nconvergence. Special care, enabled by the systematic use of rotation\nmatrices, is taken to understand the range of pitch angles for which\nall quantities in the equation are well defined. The paper provides\na fast and numerically reliable algorithm that can be used within\nanalysis tools such as those involving numerical integration of system\ndynamics.

KW - Newton method

KW - bicycle

KW - kinematics

KW - motorcycle

KW - single-track vehicles

U2 - 10.1080/00423110801966108

DO - 10.1080/00423110801966108

M3 - Article

VL - 47

SP - 221

EP - 241

JO - Vehicle System Dynamics

JF - Vehicle System Dynamics

SN - 0042-3114

IS - 2

ER -