The two-thirds power law derived from an higher-derivative action
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929588265811968 |
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| author | Boulanger, N. Buisseret, F. Dierick, F. White, O. |
| author_facet | Boulanger, N. Buisseret, F. Dierick, F. White, O. |
| contents | The two-thirds power law is a link between angular speed $ω$ and curvature $κ$ observed in voluntary human movements: $ω$ is proportional to $κ^{2/3}$. Squared jerk is known to be a Lagrangian leading to the latter law. We propose that a broader class of higher-derivative Lagrangians leads to the two-thirds power law and we perform the Hamiltonian analysis leading to action-angle variables through Ostrogradski's procedure. In this framework, squared jerk appears as an action variable and its minimization may be related to power expenditure minimization during motion. The identified higher-derivative Lagrangians are therefore natural candidates for cost functions, i.e. movement functions that are targeted to be minimal when one individual performs a voluntary movement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15503 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The two-thirds power law derived from an higher-derivative action Boulanger, N. Buisseret, F. Dierick, F. White, O. Classical Physics Biological Physics The two-thirds power law is a link between angular speed $ω$ and curvature $κ$ observed in voluntary human movements: $ω$ is proportional to $κ^{2/3}$. Squared jerk is known to be a Lagrangian leading to the latter law. We propose that a broader class of higher-derivative Lagrangians leads to the two-thirds power law and we perform the Hamiltonian analysis leading to action-angle variables through Ostrogradski's procedure. In this framework, squared jerk appears as an action variable and its minimization may be related to power expenditure minimization during motion. The identified higher-derivative Lagrangians are therefore natural candidates for cost functions, i.e. movement functions that are targeted to be minimal when one individual performs a voluntary movement. |
| title | The two-thirds power law derived from an higher-derivative action |
| topic | Classical Physics Biological Physics |
| url | https://arxiv.org/abs/2405.15503 |