Approximation Solution for the Zener Impact Theory

Collisions can be classified as completely elastic or inelastic. Collision mechanics theory has gradually developed from elastic to inelastic collision theories. Based on the Hertz elastic collision contact theory and Zener inelastic collision theory model, we derive and explain the Hertz and Zener...

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Bibliographic Details
Published inMathematics (Basel) Vol. 9; no. 18; p. 2222
Main Authors Tsai, Ping-Kun, Li, Cheng-Han, Lai, Chia-Chun, Huang, Ko-Jung, Cheng, Ching-Wei
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2021
Subjects
approximate solution
Civil engineering
Collision dynamics
Deformation
elastic collision
Elastic scattering
Equations of motion
inelastic collision
Inelastic collisions
Mathematical models
Mathematics
Nonlinear differential equations
Spheres
Velocity
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Summary:Collisions can be classified as completely elastic or inelastic. Collision mechanics theory has gradually developed from elastic to inelastic collision theories. Based on the Hertz elastic collision contact theory and Zener inelastic collision theory model, we derive and explain the Hertz and Zener collision theory model equations in detail in this study and establish the Zener inelastic collision theory, which is a simple and fast calculation of the approximate solution to the nonlinear differential equations of motion. We propose an approximate formula to obtain the Zener nonlinear differential equation of motion in a simple manner. The approximate solution determines the relevant values of the collision force, material displacement, velocity, and contact time.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9182222