{"action":"created","issue":{"url":"https://api.github.com/repos/jlblancoc/tutorial-se3-manifold/issues/2","repository_url":"https://api.github.com/repos/jlblancoc/tutorial-se3-manifold","labels_url":"https://api.github.com/repos/jlblancoc/tutorial-se3-manifold/issues/2/labels{/name}","comments_url":"https://api.github.com/repos/jlblancoc/tutorial-se3-manifold/issues/2/comments","events_url":"https://api.github.com/repos/jlblancoc/tutorial-se3-manifold/issues/2/events","html_url":"https://github.com/jlblancoc/tutorial-se3-manifold/issues/2","id":273101388,"node_id":"MDU6SXNzdWUyNzMxMDEzODg=","number":2,"title":"TO-DO: Jacobian of Matrix-to-quaternion conversion","user":{"login":"jlblancoc","id":5497818,"node_id":"MDQ6VXNlcjU0OTc4MTg=","avatar_url":"https://avatars2.githubusercontent.com/u/5497818?v=4","gravatar_id":"","url":"https://api.github.com/users/jlblancoc","html_url":"https://github.com/jlblancoc","followers_url":"https://api.github.com/users/jlblancoc/followers","following_url":"https://api.github.com/users/jlblancoc/following{/other_user}","gists_url":"https://api.github.com/users/jlblancoc/gists{/gist_id}","starred_url":"https://api.github.com/users/jlblancoc/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jlblancoc/subscriptions","organizations_url":"https://api.github.com/users/jlblancoc/orgs","repos_url":"https://api.github.com/users/jlblancoc/repos","events_url":"https://api.github.com/users/jlblancoc/events{/privacy}","received_events_url":"https://api.github.com/users/jlblancoc/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":5,"created_at":"2017-11-11T01:01:52Z","updated_at":"2018-11-06T23:41:52Z","closed_at":null,"author_association":"OWNER","body":"It might be useful to define the Jacobian for this conversion, so all formulas in latest chapters also apply to quaternions via the chain rule. \r\n\r\nThe conversion Jacobian can be derived by combining two Jacobians: \r\n* Matrix -> YPR  (see §2.5).\r\n* YPR -> Quaternion (see §2.1).\r\n\r\nA more direct way would be to derive the Jacobian of the operation described in [this paper](https://arc.aiaa.org/doi/abs/10.2514/2.4654?journalCode=jgcd), but it implies obtaining the Jacobian of an eigenvector. I couldn't find such a closed form expression, not even in the \"Matrix Bookbook\".\r\n"},"comment":{"url":"https://api.github.com/repos/jlblancoc/tutorial-se3-manifold/issues/comments/436450193","html_url":"https://github.com/jlblancoc/tutorial-se3-manifold/issues/2#issuecomment-436450193","issue_url":"https://api.github.com/repos/jlblancoc/tutorial-se3-manifold/issues/2","id":436450193,"node_id":"MDEyOklzc3VlQ29tbWVudDQzNjQ1MDE5Mw==","user":{"login":"v01d","id":161706,"node_id":"MDQ6VXNlcjE2MTcwNg==","avatar_url":"https://avatars3.githubusercontent.com/u/161706?v=4","gravatar_id":"","url":"https://api.github.com/users/v01d","html_url":"https://github.com/v01d","followers_url":"https://api.github.com/users/v01d/followers","following_url":"https://api.github.com/users/v01d/following{/other_user}","gists_url":"https://api.github.com/users/v01d/gists{/gist_id}","starred_url":"https://api.github.com/users/v01d/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/v01d/subscriptions","organizations_url":"https://api.github.com/users/v01d/orgs","repos_url":"https://api.github.com/users/v01d/repos","events_url":"https://api.github.com/users/v01d/events{/privacy}","received_events_url":"https://api.github.com/users/v01d/received_events","type":"User","site_admin":false},"created_at":"2018-11-06T23:41:52Z","updated_at":"2018-11-06T23:41:52Z","author_association":"NONE","body":"BTW: Sophus seems to implement the log() operation using equation (29) of https://arxiv.org/pdf/1107.1119.pdf which also seems reasonable to derive."}}
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