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June 20, 2026Journal of Applied MathematicsOpen Access

Modeling Height Distributions in Tilted Ellipsoids With Applications to Pennate Muscle Geometry

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Authors

RRRobert Rockenfeller

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Overview

Closed-form expressions model height distributions in tilted ellipsoids, suggesting applications in biomechanics.

Key Points

  • This research aims to develop a geometric-probabilistic framework for height distributions of tilted ellipsoids and their applications.
  • Derived closed-form expressions for height distributions in upright and tilted ellipsoids.
  • Analyzed the probability density function related to semiaxis lengths and tilt around the principal axis.
  • Unified geometric and probabilistic approaches for evaluating ellipsoidal domains.
  • The probability density function for the height Z-direction is f_Z(z)=2·z·c^−2 for 0≤z≤c.
  • Height distributions retain the same analytical form even when ellipsoids are tilted.
  • These results enable analytical estimations of mean fascicle length and variability related to pennation angle.

Cite This Study

Robert Rockenfeller (2026) studied this question.

synapsesocial.com/papers/6a362ee4db0793dc1a5367cahttps://doi.org/10.1155/jama/3099113
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