Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.19016 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916430970093568 |
|---|---|
| author | Peters, James F. Liyanage, Tharaka U. |
| author_facet | Peters, James F. Liyanage, Tharaka U. |
| contents | This paper introduces an axiomatic approach in the theory of energy dissipation in Hilbert envelopes on waveforms emanating from various vibrating systems. A Hilbert envelope is a curve tangent to peak points on a motion waveform. The basic approach is to compare non-modulated vs. modulated waveforms in measuring energy loss during the vibratory motion $m(t)$ at time $t$ of moving object such as a walker, runner or biker recorded in a video. Modulation of $m(t)$ is achieved by using Mersenne primes to adjust the frequency $ω$ of the Euler exponential in $m(t)e^{\pm j2πωt}{\rm d}t$. Expediture of energy $E_{m(t)}$ by a system is measured in terms of the area bounded by the motion $m(t)$ waveform at time $t$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy Dissipation in Hilbert Envelopes on Motion Waveforms Detected in Vibrating Systems: An Axiomatic Approach Peters, James F. Liyanage, Tharaka U. General Physics 74H80, 76F20, 93A05 This paper introduces an axiomatic approach in the theory of energy dissipation in Hilbert envelopes on waveforms emanating from various vibrating systems. A Hilbert envelope is a curve tangent to peak points on a motion waveform. The basic approach is to compare non-modulated vs. modulated waveforms in measuring energy loss during the vibratory motion $m(t)$ at time $t$ of moving object such as a walker, runner or biker recorded in a video. Modulation of $m(t)$ is achieved by using Mersenne primes to adjust the frequency $ω$ of the Euler exponential in $m(t)e^{\pm j2πωt}{\rm d}t$. Expediture of energy $E_{m(t)}$ by a system is measured in terms of the area bounded by the motion $m(t)$ waveform at time $t$. |
| title | Energy Dissipation in Hilbert Envelopes on Motion Waveforms Detected in Vibrating Systems: An Axiomatic Approach |
| topic | General Physics 74H80, 76F20, 93A05 |
| url | https://arxiv.org/abs/2409.19016 |