{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ZF4P3PKMIMGT2S2WSXTLXUOR2A","short_pith_number":"pith:ZF4P3PKM","schema_version":"1.0","canonical_sha256":"c978fdbd4c430d3d4b5695e6bbd1d1d010714f814b7cf4878334f1829e298d29","source":{"kind":"arxiv","id":"1103.2822","version":1},"attestation_state":"computed","paper":{"title":"Stable Manifolds of Saddle Points for Pendulum Dynamics on S^2 and SO(3)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Melvin Leok, N. Harris McClamroch, Taeyoung Lee","submitted_at":"2011-03-15T00:18:20Z","abstract_excerpt":"Attitude control systems naturally evolve on nonlinear configuration spaces, such as S^2 and SO(3). The nontrivial topological properties of these configuration spaces result in interesting and complicated nonlinear dynamics when studying the corresponding closed loop attitude control systems. In this paper, we review some global analysis and simulation techniques that allow us to describe the global nonlinear stable manifolds of the hyperbolic equilibria of these closed loop systems. A deeper understanding of these invariant manifold structures are critical to understanding the global stabili"},"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":"1103.2822","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-15T00:18:20Z","cross_cats_sorted":[],"title_canon_sha256":"78e5d204ed9af65956e1aa3019f16deac0023a43633495ef9ef380e1f879808f","abstract_canon_sha256":"94616054af15a371751c3355c42033d8e216f128919d3fe9c0a5161518bc4038"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:19.155587Z","signature_b64":"7QBDzZvoFgyGNaOGBM0aa1YM6H0U7ZPC491Z2uX+5z1PeT+r53yvBpTaOBaUTXbQz+E8EO9oxpsq9u6m5KdMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c978fdbd4c430d3d4b5695e6bbd1d1d010714f814b7cf4878334f1829e298d29","last_reissued_at":"2026-05-18T02:22:19.154924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:19.154924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable Manifolds of Saddle Points for Pendulum Dynamics on S^2 and SO(3)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Melvin Leok, N. Harris McClamroch, Taeyoung Lee","submitted_at":"2011-03-15T00:18:20Z","abstract_excerpt":"Attitude control systems naturally evolve on nonlinear configuration spaces, such as S^2 and SO(3). The nontrivial topological properties of these configuration spaces result in interesting and complicated nonlinear dynamics when studying the corresponding closed loop attitude control systems. In this paper, we review some global analysis and simulation techniques that allow us to describe the global nonlinear stable manifolds of the hyperbolic equilibria of these closed loop systems. A deeper understanding of these invariant manifold structures are critical to understanding the global stabili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2822","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.2822","created_at":"2026-05-18T02:22:19.155031+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.2822v1","created_at":"2026-05-18T02:22:19.155031+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2822","created_at":"2026-05-18T02:22:19.155031+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZF4P3PKMIMGT","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZF4P3PKMIMGT2S2W","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZF4P3PKM","created_at":"2026-05-18T12:26:47.523578+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZF4P3PKMIMGT2S2WSXTLXUOR2A","json":"https://pith.science/pith/ZF4P3PKMIMGT2S2WSXTLXUOR2A.json","graph_json":"https://pith.science/api/pith-number/ZF4P3PKMIMGT2S2WSXTLXUOR2A/graph.json","events_json":"https://pith.science/api/pith-number/ZF4P3PKMIMGT2S2WSXTLXUOR2A/events.json","paper":"https://pith.science/paper/ZF4P3PKM"},"agent_actions":{"view_html":"https://pith.science/pith/ZF4P3PKMIMGT2S2WSXTLXUOR2A","download_json":"https://pith.science/pith/ZF4P3PKMIMGT2S2WSXTLXUOR2A.json","view_paper":"https://pith.science/paper/ZF4P3PKM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.2822&json=true","fetch_graph":"https://pith.science/api/pith-number/ZF4P3PKMIMGT2S2WSXTLXUOR2A/graph.json","fetch_events":"https://pith.science/api/pith-number/ZF4P3PKMIMGT2S2WSXTLXUOR2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZF4P3PKMIMGT2S2WSXTLXUOR2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZF4P3PKMIMGT2S2WSXTLXUOR2A/action/storage_attestation","attest_author":"https://pith.science/pith/ZF4P3PKMIMGT2S2WSXTLXUOR2A/action/author_attestation","sign_citation":"https://pith.science/pith/ZF4P3PKMIMGT2S2WSXTLXUOR2A/action/citation_signature","submit_replication":"https://pith.science/pith/ZF4P3PKMIMGT2S2WSXTLXUOR2A/action/replication_record"}},"created_at":"2026-05-18T02:22:19.155031+00:00","updated_at":"2026-05-18T02:22:19.155031+00:00"}