{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:26RT4XKUES7OMI4JALA6K74JAZ","short_pith_number":"pith:26RT4XKU","schema_version":"1.0","canonical_sha256":"d7a33e5d5424bee6238902c1e57f89065be929dcb98651fd0666bedc4b8703e5","source":{"kind":"arxiv","id":"1210.2745","version":2},"attestation_state":"computed","paper":{"title":"The classical mechanics of non-conservative systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OC","physics.flu-dyn","physics.plasm-ph"],"primary_cat":"gr-qc","authors_text":"Chad R. Galley","submitted_at":"2012-10-09T20:30:30Z","abstract_excerpt":"Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. This subtlety can have undesirable effects. I present a formulation of Hamilton's principle that is compatible with initial value problems. Remarkably, this leads to a natural formulation for the Lagrangi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.2745","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-10-09T20:30:30Z","cross_cats_sorted":["math-ph","math.MP","math.OC","physics.flu-dyn","physics.plasm-ph"],"title_canon_sha256":"ea5cc0c107a6e0acb6e11af62cab79f1cff2343e5f72ac647b2e74f60198da97","abstract_canon_sha256":"c704da61ab9ef73da574ecf0e2732b5a8b3ac4c6842ecc2699fc85183d9cebc7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:54:03.808494Z","signature_b64":"OWRk+chJh+WsrVDXLYt6EcC1rIzIuooZtWeTSr0TNEzjOrGniOkbT5a3MuXZslEGTd2v85EEllDS3LKdo/K3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7a33e5d5424bee6238902c1e57f89065be929dcb98651fd0666bedc4b8703e5","last_reissued_at":"2026-05-18T01:54:03.808085Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:54:03.808085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The classical mechanics of non-conservative systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OC","physics.flu-dyn","physics.plasm-ph"],"primary_cat":"gr-qc","authors_text":"Chad R. Galley","submitted_at":"2012-10-09T20:30:30Z","abstract_excerpt":"Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often goes unnoticed in physics: it is formulated as a boundary value problem in time but is used to derive equations of motion that are solved with initial data. This subtlety can have undesirable effects. I present a formulation of Hamilton's principle that is compatible with initial value problems. Remarkably, this leads to a natural formulation for the Lagrangi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2745","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.2745","created_at":"2026-05-18T01:54:03.808149+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2745v2","created_at":"2026-05-18T01:54:03.808149+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2745","created_at":"2026-05-18T01:54:03.808149+00:00"},{"alias_kind":"pith_short_12","alias_value":"26RT4XKUES7O","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"26RT4XKUES7OMI4J","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"26RT4XKU","created_at":"2026-05-18T12:26:50.516681+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.09545","citing_title":"Black Hole Dynamics at Fifth Post-Newtonian Order","ref_index":57,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/26RT4XKUES7OMI4JALA6K74JAZ","json":"https://pith.science/pith/26RT4XKUES7OMI4JALA6K74JAZ.json","graph_json":"https://pith.science/api/pith-number/26RT4XKUES7OMI4JALA6K74JAZ/graph.json","events_json":"https://pith.science/api/pith-number/26RT4XKUES7OMI4JALA6K74JAZ/events.json","paper":"https://pith.science/paper/26RT4XKU"},"agent_actions":{"view_html":"https://pith.science/pith/26RT4XKUES7OMI4JALA6K74JAZ","download_json":"https://pith.science/pith/26RT4XKUES7OMI4JALA6K74JAZ.json","view_paper":"https://pith.science/paper/26RT4XKU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2745&json=true","fetch_graph":"https://pith.science/api/pith-number/26RT4XKUES7OMI4JALA6K74JAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/26RT4XKUES7OMI4JALA6K74JAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26RT4XKUES7OMI4JALA6K74JAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26RT4XKUES7OMI4JALA6K74JAZ/action/storage_attestation","attest_author":"https://pith.science/pith/26RT4XKUES7OMI4JALA6K74JAZ/action/author_attestation","sign_citation":"https://pith.science/pith/26RT4XKUES7OMI4JALA6K74JAZ/action/citation_signature","submit_replication":"https://pith.science/pith/26RT4XKUES7OMI4JALA6K74JAZ/action/replication_record"}},"created_at":"2026-05-18T01:54:03.808149+00:00","updated_at":"2026-05-18T01:54:03.808149+00:00"}