Approximation Solution for the Zener Impact Theory

Ping-Kun Tsai, Cheng-Han Li, Chia-Chun Lai, Ko-Jung Huang and Ching-Wei Cheng
Additional contact information
Ping-Kun Tsai: Department of Bio-Industrial Mechatronics Engineering, National Chung Hsing University, Taichung 402, Taiwan
Cheng-Han Li: Department of Bio-Industrial Mechatronics Engineering, National Chung Hsing University, Taichung 402, Taiwan
Chia-Chun Lai: Department of Bio-Industrial Mechatronics Engineering, National Chung Hsing University, Taichung 402, Taiwan
Ko-Jung Huang: Department of Bio-Industrial Mechatronics Engineering, National Chung Hsing University, Taichung 402, Taiwan
Ching-Wei Cheng: College of Intelligence, National Taichung University of Science and Technology, Taichung 404, Taiwan

Mathematics, 2021, vol. 9, issue 18, 1-12

Abstract: 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.

Keywords: elastic collision; inelastic collision; approximate solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/18/2222/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/18/2222/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:18:p:2222-:d:632812

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().