{"paper":{"title":"A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Roberto Castelli","submitted_at":"2013-09-06T10:53:13Z","abstract_excerpt":"This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogenous potential of degree $-2\\leq \\alpha\\leq 1$ and logarithmic potential. We derive a formula for the apsidal angle as a fixed-end points integral and we study the derivative of the apsidal angle with respect to the angular momentum $\\ell$. The monotonicity of the apsidal angle as function of $\\ell$ is discussed and it is proved in the logarithmic potential case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1594","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}