{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/118136"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/118136","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Using a Curvilinear Coordinate System for Satellite Relative Motion","abstract":"The number of dynamics needed to model the motion between a Chief and Deputy satellites has grown greatly since the introduction of the Hill, Clohessy-Wilshire (HCW) equations of motion were introduced. The models have grown to include various things like perturbations, specifically drag, J2, and solar radiation pressure. Dynamics models have also been developed that use True Anomaly as the independent variable instead of time. A lot of work has been put forth to also include cases where the Chief is in an eccentric orbit. While these models have increased the fidelity of relative dynamics these models become very complicated to implement. That is why the HCW equations remain extremely popular after all these developments. However, their simplicity causes issues when there is In-Track separation between the Chief and Deputy satellites. The error in the dynamics increases as this separation increases which leads to a typical constraint that the separation between the Chief and Deputy needs to be much smaller than the radius of the Chief's orbit. That is where this works starts, by examining into ways to increase the accuracy in the HCW equations as the In-Track separation between the Chief and Deputy grows. In which, this will be done by using a curvilinear coordinate system. Furthermore, a technique of using a Virtual Chief satellite will by employed to allow for the HCW equations to be valid for cases where the Chief is in an eccentric orbit.","abstract_html":"The number of dynamics needed to model the motion between a Chief and Deputy satellites has grown greatly since the introduction of the Hill, Clohessy-Wilshire (HCW) equations of motion were introduced. The models have grown to include various things like perturbations, specifically drag, J2, and solar radiation pressure. Dynamics models have also been developed that use True Anomaly as the independent variable instead of time. A lot of work has been put forth to also include cases where the Chief is in an eccentric orbit. While these models have increased the fidelity of relative dynamics these models become very complicated to implement. That is why the HCW equations remain extremely popular after all these developments. However, their simplicity causes issues when there is In-Track separation between the Chief and Deputy satellites. The error in the dynamics increases as this separation increases which leads to a typical constraint that the separation between the Chief and Deputy needs to be much smaller than the radius of the Chief's orbit. That is where this works starts, by examining into ways to increase the accuracy in the HCW equations as the In-Track separation between the Chief and Deputy grows. In which, this will be done by using a curvilinear coordinate system. Furthermore, a technique of using a Virtual Chief satellite will by employed to allow for the HCW equations to be valid for cases where the Chief is in an eccentric orbit.","abstract_has_math":false,"creators":["Midas, Alex Matthew"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Aerospace Engineering","degree_department":"Aerospace and Ocean Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Schroeder, Kevin Kent"],"committee_members":["Fitzgerald, Riley McCrea","Black, Jonathan T."],"year":2024,"date_issued":"2024-02-23","date_published":"2024-02-23","updated_at":"2026-07-22T22:18:49Z","subjects":["Relative Motion","RPO","Curvilinear","Virtual Chief","Ghost Chief"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:39411"],"render_values":[{"text":"vt_gsexam:39411","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10919/118136","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Schroeder, Kevin Kent"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Fitzgerald, Riley McCrea","Black, Jonathan T."]},{"key":"dc:contributor.department","label":"Department","values":["Aerospace and Ocean Engineering"]},{"key":"dc:creator","label":"Author","values":["Midas, Alex Matthew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-02-24T09:00:37Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-02-24T09:00:37Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-02-23"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Relative Motion","RPO","Curvilinear","Virtual Chief","Ghost Chief"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:39411"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/118136"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The number of dynamics needed to model the motion between a Chief and Deputy satellites has grown greatly since the introduction of the Hill, Clohessy-Wilshire (HCW) equations of motion were introduced. The models have grown to include various things like perturbations, specifically drag, J2, and solar radiation pressure. Dynamics models have also been developed that use True Anomaly as the independent variable instead of time. A lot of work has been put forth to also include cases where the Chief is in an eccentric orbit. While these models have increased the fidelity of relative dynamics these models become very complicated to implement. That is why the HCW equations remain extremely popular after all these developments. However, their simplicity causes issues when there is In-Track separation between the Chief and Deputy satellites. The error in the dynamics increases as this separation increases which leads to a typical constraint that the separation between the Chief and Deputy needs to be much smaller than the radius of the Chief's orbit. That is where this works starts, by examining into ways to increase the accuracy in the HCW equations as the In-Track separation between the Chief and Deputy grows. In which, this will be done by using a curvilinear coordinate system. Furthermore, a technique of using a Virtual Chief satellite will by employed to allow for the HCW equations to be valid for cases where the Chief is in an eccentric orbit."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["There are many different models that are used to model the relative motion between two satellites. These models vary from low to high fidelity in the different types of perturbation and ranges that they can model. These higher fidelity models because very complex to implement and while useful the low fidelity models are still popular, specifically the HCW equations. This thesis works on making the HCW equations valid for a larger range of cases."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Using a Curvilinear Coordinate System for Satellite Relative Motion"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Schroeder, Kevin Kent"],"dc:contributor.committeemember":["Fitzgerald, Riley McCrea","Black, Jonathan T."],"dc:contributor.department":["Aerospace and Ocean Engineering"],"dc:creator":["Midas, Alex Matthew"],"dc:date.accessioned":["2024-02-24T09:00:37Z"],"dc:date.available":["2024-02-24T09:00:37Z"],"dc:date.issued":["2024-02-23"],"dc:description.abstract":["The number of dynamics needed to model the motion between a Chief and Deputy satellites has grown greatly since the introduction of the Hill, Clohessy-Wilshire (HCW) equations of motion were introduced. The models have grown to include various things like perturbations, specifically drag, J2, and solar radiation pressure. Dynamics models have also been developed that use True Anomaly as the independent variable instead of time. A lot of work has been put forth to also include cases where the Chief is in an eccentric orbit. While these models have increased the fidelity of relative dynamics these models become very complicated to implement. That is why the HCW equations remain extremely popular after all these developments. However, their simplicity causes issues when there is In-Track separation between the Chief and Deputy satellites. The error in the dynamics increases as this separation increases which leads to a typical constraint that the separation between the Chief and Deputy needs to be much smaller than the radius of the Chief's orbit. That is where this works starts, by examining into ways to increase the accuracy in the HCW equations as the In-Track separation between the Chief and Deputy grows. In which, this will be done by using a curvilinear coordinate system. Furthermore, a technique of using a Virtual Chief satellite will by employed to allow for the HCW equations to be valid for cases where the Chief is in an eccentric orbit."],"dc:description.abstractgeneral":["There are many different models that are used to model the relative motion between two satellites. These models vary from low to high fidelity in the different types of perturbation and ranges that they can model. These higher fidelity models because very complex to implement and while useful the low fidelity models are still popular, specifically the HCW equations. This thesis works on making the HCW equations valid for a larger range of cases."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:39411"],"dc:identifier.uri":["https://hdl.handle.net/10919/118136"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Relative Motion","RPO","Curvilinear","Virtual Chief","Ghost Chief"],"dc:title":["Using a Curvilinear Coordinate System for Satellite Relative Motion"],"dc:type":["Thesis"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:18:49Z"}