{"version":9,"randomSeed":"25dec9346a75efc880595a465bbf32e6","graph":{"viewport":{"xmin":-24.434862658977604,"ymin":-37.56346543931116,"xmax":47.00452261181721,"ymax":22.52502557182877}},"expressions":{"list":[{"type":"folder","id":"16","title":"setup","hidden":true,"collapsed":true},{"type":"text","id":"3","folderId":"16","text":"masses of objects"},{"type":"expression","id":"4","folderId":"16","color":"#388c46","latex":"M=\\left[20,1,0.5,4\\right]"},{"type":"text","id":"6","folderId":"16","text":"initial positions"},{"type":"expression","id":"7","folderId":"16","color":"#000000","latex":"P_{o}=\\left[\\left(0,0\\right),\\left(6,0\\right),\\left(0,10\\right),\\left(0,-8\\right)\\right]"},{"type":"text","id":"11","folderId":"16","text":"initial velocities (vectors)"},{"type":"expression","id":"12","folderId":"16","color":"#388c46","latex":"V_{o}=\\left[\\left(0,0\\right),\\left(0,-2\\right),\\left(1.2,0\\right),\\left(-2,0\\right)\\right]"},{"type":"text","id":"72","folderId":"16","text":"diametres"},{"type":"expression","id":"73","folderId":"16","color":"#2d70b3","latex":"D=\\left[3,0.8,1.3,2\\right]"},{"type":"text","id":"68","folderId":"16","text":"colours"},{"type":"expression","id":"69","folderId":"16","color":"#6042a6","latex":"C=\\left[\\operatorname{rgb}\\left(255,200,0\\right),\\operatorname{rgb}\\left(100,100,100\\right),\\operatorname{rgb}\\left(150,50,50\\right),\\operatorname{rgb}\\left(150,0,200\\right)\\right]"},{"type":"text","id":"34","folderId":"16","text":"time interval"},{"type":"expression","id":"35","folderId":"16","color":"#2d70b3","latex":"d_{t}=0.1"},{"type":"text","id":"43","folderId":"16","text":"gravitational constant"},{"type":"expression","id":"44","folderId":"16","color":"#388c46","latex":"G=1"},{"type":"folder","id":"18","title":"running data","collapsed":true},{"type":"text","id":"20","folderId":"18","text":"current positions"},{"type":"expression","id":"27","folderId":"18","color":"#2d70b3","latex":"P=\\left[\\left(0.052726230008838755,-0.5237362528614022\\right),\\left(1.6623206157231207,-6.759555635466723\\right),\\left(4.7619546799129,8.157162494552022\\right),\\left(-7.544455638964087,-5.56107513864531\\right)\\right]","hidden":true,"colorLatex":"C","pointSize":"20"},{"type":"expression","id":"70","folderId":"18","color":"#000000","latex":"\\operatorname{distance}\\left(\\left(x,y\\right),P\\right)\\le\\frac{1}{2}D","colorLatex":"C","fillOpacity":"1"},{"type":"text","id":"29","folderId":"18","text":"current velocities"},{"type":"expression","id":"30","folderId":"18","color":"#6042a6","latex":"V=\\left[\\left(-0.018817898557591986,-0.24599017958881877\\right),\\left(-1.8046318205652447,-0.8246974972302628\\right),\\left(0.9853763596378949,-0.8810556055198451\\right),\\left(-1.427924597025466,1.0462572229416403\\right)\\right]","hidden":true},{"type":"text","id":"59","folderId":"18","text":"visualise velocities"},{"type":"expression","id":"60","folderId":"18","color":"#c74440","latex":"\\left[\\operatorname{polygon}\\left(P\\left[a\\right],P\\left[a\\right]+V\\left[a\\right]\\right)\\operatorname{for}a=\\left[1,2,...\\operatorname{length}\\left(P\\right)\\right]\\right]"},{"type":"folder","id":"23","title":"actions","collapsed":true},{"type":"text","id":"25","folderId":"23","text":"reset"},{"type":"expression","id":"26","folderId":"23","color":"#c74440","latex":"R=\\left(P\\to P_{o},V\\to V_{o}\\right)"},{"type":"text","id":"48","folderId":"23","text":"normalise vector"},{"type":"expression","id":"46","folderId":"23","color":"#000000","latex":"N\\left(v\\right)=\\frac{v}{\\operatorname{distance}\\left(\\left(0,0\\right),v\\right)+\\left\\{\\operatorname{distance}\\left(\\left(0,0\\right),v\\right)=0:1,0\\right\\}}"},{"type":"text","id":"51","folderId":"23","text":"total acceleration on object (index i)"},{"type":"expression","id":"52","folderId":"23","color":"#6042a6","latex":"A\\left(i\\right)=\\left(\\sum_{k=1}^{\\operatorname{length}\\left(M\\right)}\\frac{\\left\\{i=k:0,1\\right\\}\\cdot M\\left[k\\right]N\\left(P\\left[k\\right]-P\\left[i\\right]\\right).x}{\\operatorname{distance}\\left(P\\left[k\\right],P\\left[i\\right]\\right)^{2}+\\left\\{i=k:1,0\\right\\}},\\sum_{k=1}^{\\operatorname{length}\\left(M\\right)}\\frac{\\left\\{i=k:0,1\\right\\}\\cdot M\\left[k\\right]N\\left(P\\left[k\\right]-P\\left[i\\right]\\right).y}{\\operatorname{distance}\\left(P\\left[k\\right],P\\left[i\\right]\\right)^{2}+\\left\\{i=k:1,0\\right\\}}\\right)G"},{"type":"text","id":"32","folderId":"23","text":"step of time"},{"type":"expression","id":"36","folderId":"23","color":"#388c46","latex":"T=\\left(P\\to P+d_{t}V,V\\to V+d_{t}A\\left(\\left[1,2,...\\operatorname{length}\\left(M\\right)\\right]\\right)\\right)"},{"type":"expression","id":"63","color":"#6042a6","latex":"R"}],"ticker":{"handlerLatex":"T","minStepLatex":"0","open":true}}}