Geometry of motion and nutation stability of free axisymmetric variable mass systems
In classical mechanics, the ‘geometry of motion’ refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is developed. An analytic solution to the second Euler angle characteriz...
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| Published in | Nonlinear dynamics Vol. 94; no. 3; pp. 2205 - 2218 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.11.2018
Springer Nature B.V |
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| Abstract | In classical mechanics, the ‘geometry of motion’ refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is developed. An analytic solution to the second Euler angle characterizing nutation naturally falls out of this method, without explicitly solving the nonlinear differential equations of motion. This is used to examine the coning motion of a free axisymmetric cylinder subject to three idealized models of mass loss and new insight into their rotational stability is presented. It is seen that the angular speeds for some configurations of these cylinders grow without bounds. In spite of this phenomenon, all configurations explored here are seen to exhibit nutational stability, a desirable property in solid rocket motors. |
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| AbstractList | In classical mechanics, the ‘geometry of motion’ refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is developed. An analytic solution to the second Euler angle characterizing nutation naturally falls out of this method, without explicitly solving the nonlinear differential equations of motion. This is used to examine the coning motion of a free axisymmetric cylinder subject to three idealized models of mass loss and new insight into their rotational stability is presented. It is seen that the angular speeds for some configurations of these cylinders grow without bounds. In spite of this phenomenon, all configurations explored here are seen to exhibit nutational stability, a desirable property in solid rocket motors. |
| Author | Nanjangud, Angadh |
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| Cites_doi | 10.2514/6.1986-2271 10.1007/s11071-007-9275-5(2007) 10.2514/3.20837 10.1007/s11071-008-9362-2 10.1007/BF03546265 10.1115/1.2896025 10.2514/3.21525 10.2514/2.4556 10.2514/1.A33152 10.1115/1.1653738 10.1007/s40295-016-0099-8 10.2514/6.1985-1382 10.2514/3.29262 10.1016/j.ast.2018.03.003 10.2514/3.3544 10.2514/2.3586 10.2514/1.59686 10.2514/1.62695 10.1115/1.2896031 |
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| References | MaoTCEkeFOAttitude dynamics of a torque-free variable mass cylindrical bodyJ. Astronaut. Sci.200048435448 WangS-MEkeFORotational dynamics of axisymmetric variable mass systemsJ. Appl. Mech.199562497097410.1115/1.2896031 LikinsPWElements of Engineering Mechanics1973New YorkMcGraw-Hill0368.70001 Nanjangud, A.: On the rotational dynamics of variable mass systems. Ph.D. dissertation, University of California, Davis (2016) AyoubiMAMartinKMLonguskiJMAnalytical solution for spinning thrusting spacecraft with transverse ramp-up torquesJ. Guid. Control Dyn.20143741272128210.2514/1.62695 WebsterEActive Nutation Control for Spinning Solid Motor Upper Stages1985Monterey, CAAmerican Institute of Aeronautics and Astronautics10.2514/6.1985-1382 BanerjeeAKDynamics of a variable-mass, flexible-body systemJ. Guid. Control Dyn.20002350150810.2514/2.4556 BarkleyRJNewtonRRGrossGLMathematical Theory of Rocket Flight1947New YorkMcGraw-Hill HalsmerDMMingoriDLNutational stability and passive control of spinning rockets with internal mass motionJ. Guid. Control Dyn.19951851197120310.2514/3.21525 NanjangudAEkeFOLagrange’s equations for rocket-type variable mass systemsInt. Rev. Aerosp. Eng.201255256260 DjerassiSAlgorithm for simulation of motions of variable-mass systemsJ. Guid. Control Dyn.199821427434 ThomsonWTEquations of motion for the variable mass systemAIAA J.19664766768 EkeFOMaoT-CMorrisMJFree attitude motions of a spinning body with substantial mass lossJ. Appl. Mech.200471219019410.1115/1.1653738 ReiterGThomsonWJet damping of a solid rocket-theory and flight resultsAIAA J.19653413417 CveticaninLDynamics of body separationanalytical procedureNonlinear Dyn.2007553269278239085910.1007/s11071-008-9362-2 NanjangudAEkeFOApproximate solution to the angular speeds of a nearly-symmetric mass-varying cylindrical bodyJ. Astronaut. Sci.20176429911710.1007/s40295-016-0099-8 ThomsonWTIntroduction to Space Dynamics1986New YorkDover CochranJEJrKangJYNonlinear stability analysis of the attitude motion of a spin-stabilized upper stageAdv. Astronaut. Sci.1991751345364 HuPRenGMultibody dynamics of flexible liquid rockets with depleting propellantJ. Guid. Control Dyn.2013361840184910.2514/1.59686 EkeFOWangS-MAttitude behavior of a variable mass cylinderJ. Appl. Mech.199562493594010.1115/1.2896025 HaJCVDJanssensFLJet-damping and misalignment effects during solid rocket motor burnJ. Guid. Control Dyn.200528412420 KaplanMHModern Spacecraft Dynamics and Control1976New YorkWiley NanjangudAEkeFOAngular momentum of free variable mass systems is partially conservedAerosp. Sci. Technol.201810.1016/j.ast.2018.03.003 SnyderVWWarnerGGA re-evaluation of jet dampingJ. Spacecr. Rockets1968536436610.2514/3.29262 CveticaninLDjukicDMotion of body with discontinual mass variationNonlinear Dyn.200852324926110.1007/s11071-007-9275-5(2007)1170.70383 MartinKMLonguskiJMVelocity pointing error reduction for spinning, thrusting spacecraft via heuristic thrust profilesJ. Spacecr. Rockets20155241268127210.2514/1.A33152 Mingori, D., Yam, Y.: Nutational Stability of a Spinning Spacecraft with Internal Mass Motion and Axial Thrust. AIAA Paper 86-2271 AIAA Astrodynamics Conference Proceedings (Williamsburg, VA), pp. 367-375. AIAA, Washington, DC (1986) OrACRotor-pendulum model for the perigee assist module nutation anomalyJ. Guid. Control Dyn.199215229730310.2514/3.20837 JavorsekDLonguskiJMVelocity pointing errors associated with spinning thrusting spacecraftJ. Spacecr. Rockets200037335936510.2514/2.3586 Flandro, G.A., Van Moorhem, W.K., Shorthill, R., Chen, K., Woolsey, M.: Fluid Mechanics of Spinning Rockets. U.S. Air Force Rocket Propulsion Lab. Rept. TR-86-072, Edwards AFB, CA (1987) MeyerRXConvective instability in solid propellant rocket motorsAdv. Astronaut. Sci.198354173(AAS Paper 83-368) DM Halsmer (4485_CR29) 1995; 18 MH Kaplan (4485_CR18) 1976 WT Thomson (4485_CR4) 1986 FO Eke (4485_CR11) 1995; 62 P Hu (4485_CR8) 2013; 36 RX Meyer (4485_CR25) 1983; 54 L Cveticanin (4485_CR9) 2008; 52 A Nanjangud (4485_CR22) 2018 AK Banerjee (4485_CR7) 2000; 23 MA Ayoubi (4485_CR19) 2014; 37 RJ Barkley (4485_CR1) 1947 G Reiter (4485_CR2) 1965; 3 KM Martin (4485_CR20) 2015; 52 A Nanjangud (4485_CR5) 2012; 5 4485_CR14 WT Thomson (4485_CR3) 1966; 4 TC Mao (4485_CR31) 2000; 48 JE Cochran Jr (4485_CR26) 1991; 75 E Webster (4485_CR30) 1985 S-M Wang (4485_CR12) 1995; 62 PW Likins (4485_CR17) 1973 VW Snyder (4485_CR24) 1968; 5 A Nanjangud (4485_CR16) 2017; 64 D Javorsek (4485_CR21) 2000; 37 S Djerassi (4485_CR6) 1998; 21 4485_CR23 JCVD Ha (4485_CR15) 2005; 28 L Cveticanin (4485_CR10) 2007; 55 FO Eke (4485_CR13) 2004; 71 4485_CR28 AC Or (4485_CR27) 1992; 15 |
| References_xml | – reference: WangS-MEkeFORotational dynamics of axisymmetric variable mass systemsJ. Appl. Mech.199562497097410.1115/1.2896031 – reference: EkeFOMaoT-CMorrisMJFree attitude motions of a spinning body with substantial mass lossJ. Appl. Mech.200471219019410.1115/1.1653738 – reference: Nanjangud, A.: On the rotational dynamics of variable mass systems. Ph.D. dissertation, University of California, Davis (2016) – reference: BarkleyRJNewtonRRGrossGLMathematical Theory of Rocket Flight1947New YorkMcGraw-Hill – reference: ReiterGThomsonWJet damping of a solid rocket-theory and flight resultsAIAA J.19653413417 – reference: KaplanMHModern Spacecraft Dynamics and Control1976New YorkWiley – reference: OrACRotor-pendulum model for the perigee assist module nutation anomalyJ. Guid. Control Dyn.199215229730310.2514/3.20837 – reference: ThomsonWTEquations of motion for the variable mass systemAIAA J.19664766768 – reference: BanerjeeAKDynamics of a variable-mass, flexible-body systemJ. Guid. Control Dyn.20002350150810.2514/2.4556 – reference: WebsterEActive Nutation Control for Spinning Solid Motor Upper Stages1985Monterey, CAAmerican Institute of Aeronautics and Astronautics10.2514/6.1985-1382 – reference: NanjangudAEkeFOLagrange’s equations for rocket-type variable mass systemsInt. Rev. Aerosp. Eng.201255256260 – reference: ThomsonWTIntroduction to Space Dynamics1986New YorkDover – reference: SnyderVWWarnerGGA re-evaluation of jet dampingJ. Spacecr. Rockets1968536436610.2514/3.29262 – reference: HalsmerDMMingoriDLNutational stability and passive control of spinning rockets with internal mass motionJ. Guid. Control Dyn.19951851197120310.2514/3.21525 – reference: DjerassiSAlgorithm for simulation of motions of variable-mass systemsJ. Guid. Control Dyn.199821427434 – reference: Mingori, D., Yam, Y.: Nutational Stability of a Spinning Spacecraft with Internal Mass Motion and Axial Thrust. AIAA Paper 86-2271 AIAA Astrodynamics Conference Proceedings (Williamsburg, VA), pp. 367-375. AIAA, Washington, DC (1986) – reference: HuPRenGMultibody dynamics of flexible liquid rockets with depleting propellantJ. Guid. Control Dyn.2013361840184910.2514/1.59686 – reference: HaJCVDJanssensFLJet-damping and misalignment effects during solid rocket motor burnJ. Guid. Control Dyn.200528412420 – reference: MartinKMLonguskiJMVelocity pointing error reduction for spinning, thrusting spacecraft via heuristic thrust profilesJ. Spacecr. Rockets20155241268127210.2514/1.A33152 – reference: CveticaninLDynamics of body separationanalytical procedureNonlinear Dyn.2007553269278239085910.1007/s11071-008-9362-2 – reference: MaoTCEkeFOAttitude dynamics of a torque-free variable mass cylindrical bodyJ. Astronaut. Sci.200048435448 – reference: CochranJEJrKangJYNonlinear stability analysis of the attitude motion of a spin-stabilized upper stageAdv. Astronaut. Sci.1991751345364 – reference: JavorsekDLonguskiJMVelocity pointing errors associated with spinning thrusting spacecraftJ. Spacecr. Rockets200037335936510.2514/2.3586 – reference: CveticaninLDjukicDMotion of body with discontinual mass variationNonlinear Dyn.200852324926110.1007/s11071-007-9275-5(2007)1170.70383 – reference: EkeFOWangS-MAttitude behavior of a variable mass cylinderJ. Appl. Mech.199562493594010.1115/1.2896025 – reference: MeyerRXConvective instability in solid propellant rocket motorsAdv. Astronaut. Sci.198354173(AAS Paper 83-368) – reference: Flandro, G.A., Van Moorhem, W.K., Shorthill, R., Chen, K., Woolsey, M.: Fluid Mechanics of Spinning Rockets. U.S. Air Force Rocket Propulsion Lab. Rept. TR-86-072, Edwards AFB, CA (1987) – reference: NanjangudAEkeFOApproximate solution to the angular speeds of a nearly-symmetric mass-varying cylindrical bodyJ. Astronaut. Sci.20176429911710.1007/s40295-016-0099-8 – reference: NanjangudAEkeFOAngular momentum of free variable mass systems is partially conservedAerosp. Sci. Technol.201810.1016/j.ast.2018.03.003 – reference: AyoubiMAMartinKMLonguskiJMAnalytical solution for spinning thrusting spacecraft with transverse ramp-up torquesJ. Guid. Control Dyn.20143741272128210.2514/1.62695 – reference: LikinsPWElements of Engineering Mechanics1973New YorkMcGraw-Hill0368.70001 – ident: 4485_CR28 doi: 10.2514/6.1986-2271 – volume: 52 start-page: 249 issue: 3 year: 2008 ident: 4485_CR9 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-007-9275-5(2007) – volume: 15 start-page: 297 issue: 2 year: 1992 ident: 4485_CR27 publication-title: J. Guid. Control Dyn. doi: 10.2514/3.20837 – volume: 21 start-page: 427434 year: 1998 ident: 4485_CR6 publication-title: J. Guid. Control Dyn. – volume: 55 start-page: 269 issue: 3 year: 2007 ident: 4485_CR10 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-008-9362-2 – volume: 48 start-page: 435 year: 2000 ident: 4485_CR31 publication-title: J. Astronaut. Sci. doi: 10.1007/BF03546265 – volume: 62 start-page: 935 issue: 4 year: 1995 ident: 4485_CR11 publication-title: J. Appl. Mech. doi: 10.1115/1.2896025 – volume-title: Mathematical Theory of Rocket Flight year: 1947 ident: 4485_CR1 – volume-title: Modern Spacecraft Dynamics and Control year: 1976 ident: 4485_CR18 – volume: 18 start-page: 1197 issue: 5 year: 1995 ident: 4485_CR29 publication-title: J. Guid. Control Dyn. doi: 10.2514/3.21525 – volume: 5 start-page: 256 issue: 5 year: 2012 ident: 4485_CR5 publication-title: Int. Rev. Aerosp. Eng. – volume: 23 start-page: 501 year: 2000 ident: 4485_CR7 publication-title: J. Guid. Control Dyn. doi: 10.2514/2.4556 – volume-title: Introduction to Space Dynamics year: 1986 ident: 4485_CR4 – volume: 52 start-page: 1268 issue: 4 year: 2015 ident: 4485_CR20 publication-title: J. Spacecr. Rockets doi: 10.2514/1.A33152 – volume: 71 start-page: 190 issue: 2 year: 2004 ident: 4485_CR13 publication-title: J. Appl. Mech. doi: 10.1115/1.1653738 – volume: 64 start-page: 99 issue: 2 year: 2017 ident: 4485_CR16 publication-title: J. Astronaut. Sci. doi: 10.1007/s40295-016-0099-8 – volume: 75 start-page: 345 issue: 1 year: 1991 ident: 4485_CR26 publication-title: Adv. Astronaut. Sci. – volume: 28 start-page: 412420 year: 2005 ident: 4485_CR15 publication-title: J. Guid. Control Dyn. – ident: 4485_CR23 – volume-title: Elements of Engineering Mechanics year: 1973 ident: 4485_CR17 – volume-title: Active Nutation Control for Spinning Solid Motor Upper Stages year: 1985 ident: 4485_CR30 doi: 10.2514/6.1985-1382 – volume: 3 start-page: 413417 year: 1965 ident: 4485_CR2 publication-title: AIAA J. – volume: 5 start-page: 364 year: 1968 ident: 4485_CR24 publication-title: J. Spacecr. Rockets doi: 10.2514/3.29262 – year: 2018 ident: 4485_CR22 publication-title: Aerosp. Sci. Technol. doi: 10.1016/j.ast.2018.03.003 – volume: 4 start-page: 766768 year: 1966 ident: 4485_CR3 publication-title: AIAA J. doi: 10.2514/3.3544 – ident: 4485_CR14 – volume: 37 start-page: 359 issue: 3 year: 2000 ident: 4485_CR21 publication-title: J. Spacecr. Rockets doi: 10.2514/2.3586 – volume: 36 start-page: 1840 year: 2013 ident: 4485_CR8 publication-title: J. Guid. Control Dyn. doi: 10.2514/1.59686 – volume: 54 start-page: 173 year: 1983 ident: 4485_CR25 publication-title: Adv. Astronaut. Sci. – volume: 37 start-page: 1272 issue: 4 year: 2014 ident: 4485_CR19 publication-title: J. Guid. Control Dyn. doi: 10.2514/1.62695 – volume: 62 start-page: 970 issue: 4 year: 1995 ident: 4485_CR12 publication-title: J. Appl. Mech. doi: 10.1115/1.2896031 |
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| SubjectTerms | Angular speed Automotive Engineering Axisymmetric bodies Classical Mechanics Configurations Coning motion Control Cylinders Dynamical Systems Engineering Equations of motion Euler angles Exact solutions Mechanical Engineering Motion stability Nonlinear differential equations Nonlinear equations Nutation Original Paper Rocket engines Solid propellant rocket engines Variable mass systems Vibration |
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| Title | Geometry of motion and nutation stability of free axisymmetric variable mass systems |
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