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["SIM: HOOKE'S LAW ORBITS"]
["v4 — RK2 integration; plots (x,y),ℓ, ω, E, rCM; animation; massless spring; circ orb RPM calc; masses have size",null,null,null,null,null,null,null,null,null,"REFERENCE LIST"]
[null,null,null,null,null,null,null,null,null,null,null,"k","length L","L"]
["Physical Setup",null,null,null,null,"Rotation Parameters",null,null,null,null,"Spring","N/m","m","m"]
["mass A",0.99099999999999999,"kg",null,null,"ωo",51,"RPM (pos=CCW)",null,null,1,10.351927252747252,0.18732499999999999]
["CM-hook distance for mass A",4.8000000000000001E-2,"m",null,null,"initial rotation axis",0.08,"m (from mass A)",null,null,2,183.14063999999999,0.15081249999999999]
["mass B",0.49399999999999999,"kg",null,null,"initial mass separation",0.24,"m",null,null,3,24.24922193979933,7.1437500000000001E-2,9.4E-2]
["CM-hook distance for mass B",4.0500000000000001E-2,"m",null,null,"ωo",{"$f":"RPMo*PI()/30","v":5.3407075111026483},"rad/sec",null,null,4,183.14063999999999,0.10794999999999999,0.11600000000000001]
["unstretched length of spring ",9.4E-2,"m",null,null,"initially CM is",{"$f":"initaxis+Calcs!AE7","v":7.9838383838383833E-2},"m (from mass A)",null,null,5,40.240113179723501,0.10001249999999999]
["spring constant",24.2,"N/m",null,null,"ωc",{"$f":"SQRT(k*(Li-L-CA-CB)*(1+MA/MB)/(MA*Li))","v":4.1937149673396386},"rad/sec =",{"$f":"G10*30/PI()","v":40.047028018234194},"RPM",6,9.9613497795364605,0.14604999999999999]
["timestep",{"$f":"1/300","v":3.3333333333333335E-3},"sec",null,null,"Tosc,0",{"$f":"2*PI()*SQRT((MB*MA)/(MA+MB)/k)","v":0.73334656189230418},"sec",null,null,7,139.75620000000001,9.3662499999999996E-2]
["reduced mass",{"$f":"(MA*MB)/(MA+MB)","v":0.32966599326599327},"kg",null,null,"Trot,0",{"$f":"60/RPMo","v":1.1764705882352942},"sec",null,null,8,41.586011822660097,6.3500000000000001E-2]
[null,null,null,null,null,null,null,null,null,null,9,6.0763565217391298,0.117475,0.1]
[null,null,null,null,null,"xi","yi","vix","viy",null,10,27.565966753246755,5.8737499999999998E-2,6.5000000000000002E-2]
["non-conservation of E",{"$f":"(MAX(Calcs!AO7:AO1807)-MIN(Calcs!AO7:AO1807))/AVERAGE(Calcs!AO7:AO1807)","v":6.8473886522951992E-5},null,null,null,"(m)","(m)","(m/sec)","(m/sec)"]
["non-conservation of ang mom",{"$f":"(MAX(Calcs!AT9:AT1807)-MIN(Calcs!AT9:AT1807))/AVERAGE(Calcs!AT9:AT1807)","v":1.6206511674037683E-2},null,null,null,{"$f":"-initaxis","v":-0.08},0,0,{"$f":"-initaxis*radperseci","v":-0.42725660088821188},null,"Mass","kg","C"]
[null,null,null,null,null,{"$f":"Li-initaxis","v":0.15999999999999998},0,0,{"$f":"(Li-initaxis)*radperseci","v":0.85451320177642365},null,"A",0.99099999999999999,4.8000000000000001E-2]
[null,null,null,null,null,null,null,null,null,null,"B",0.49399999999999999,4.0500000000000001E-2]
[null,null,null,null,null,null,null,null,null,null,"C",0.19600000000000001,3.1E-2]
[null,null,null,null,null,null,null,null,null,null,"D",9.4E-2,3.3500000000000002E-2]

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[]
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[]
["half-timestep"]
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[]
["even rows are the half-steps in Runge-Kutta 2nd-order integration"]
["when changing formulas in rows 8 & 9, copy BOTH rows down to maintain alternation of half- and full-timesteps"]
[null,"Mass A",null,null,null,null,null,null,null,null,null,null,null,"Mass B",null,null,null,null,null,null,null,null,null,null,null,"RELATIVE POSITIONS",null,null,null,null,"CENTER OF MASS",null,null,null,null,null,null,null,null,"ENERGY",null,null,"ANGULAR MOMENTUM"]
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[null,"to do: "]
["DONE","increase # rows so 30 fps * 30 sec = 900 rows"]
["DONE","study E; if conserved better than 1%, no need to shorten dt"]
["DONE","determine when spring is compressed and thus in danger of buckling"]
["DONE","be more sophisticated with the numerical integration (see 2)"]
["DONE","plot L and angular velocity (around cm,or mass A?)"]
[3,"model spring damping?"]
[2,"include spring mass correction"]
["DONE","highlight one timestep;animate"]