Velocity Fields: Potential Visualization

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2016-11-05 16:29

In collections UQ-Applied Mathematical Analysis

This example demonstrates the graphical representation of potential fields within velocity fields, revealing core concepts in fluid dynamics or physical fields through dynamic visualization of vector fields and potential functions. Key math concepts include vector fields, potential functions, derivatives, limits, and differential equations. Construction highlights the use of GeoGebra commands/objects like Derivative (for derivative calculations), Sequence (for sequence generation), Textfield (for text input), and Plane (for plane definition). Suitable for university physics, engineering mechanics, or advanced mathematics education and exploration.

GeoGebra Commands & Parameters

Derivative((-Pot(x, y)), x) → F
Derivative((-Pot(x, y)), y) → G
Sequence((x(Element[A, i]), y(Element[A, i]), Pot(x(Element[A, i]), y(Element[A, i]))), i, 1, n) → ZA
Sequence(Sequence[Vector[(j, k), (j + (scale * F(j, k)), k + (scale * G(j, k)))], j, xmin, xmax, xstep], k, ymin, ymax, ystep) → field, {{(0.050768254456645234, 0.04182611872848607), (0.05163855865332412, 0.054698310911191594), (0.04795301573206068, 0.07111214264811228), (0.035967139113809665, 0.08889605405969991), (0.013702414243129124, 0.10160028742774685), (-0.013702414243129013, 0.10160028742774685), (-0.035967139113809665, 0.08889605405969991), (-0.047953015732060456, 0.07111214264811272), (-0.05163855865332412, 0.054698310911191594), (-0.050768254456645234, 0.04182611872848607)}, {(0.0608005750237699, 0.038537738209510675), (0.06584740126057076, 0.053661356222088674), (0.06665110726115575, 0.0760428541934095), (0.05539322350015552, 0.10533105377681062), (0.022868318524108144, 0.13045336248979789), (-0.022868318524107922, 0.13045336248979789), (-0.05539322350015552, 0.10533105377681107), (-0.06665110726115575, 0.0760428541934095), (-0.06584740126057076, 0.053661356222088674), (-0.0608005750237699, 0.038537738209510675)}, {(0.07120250793719496, 0.031600608004954456), (0.08266266010547563, 0.04716870945953655), (0.09364587512779754, 0.0748102843350471), (0.09221299546050243, 0.12277601478926714), (0.04524120071974669, 0.18070775060216882), (-0.0452412007197463, 0.18070775060216904), (-0.09221299546050243, 0.12277601478926736), (-0.09364587512779754, 0.07481028433504733), (-0.08266266010547563, 0.04716870945953677), (-0.07120250793719496, 0.03160060800495468)}, {(0.08007009503268847, 0.02032081957268983), (0.09903371862324573, 0.03231457377154601), (0.1269225345190832, 0.057980521450762934), (0.16185727131529482, 0.1232322406605082), (0.12337729774639195, 0.2818049641707342), (-0.12337729774639111, 0.2818049641707352), (-0.16185727131529504, 0.12323224066050875), (-0.12692253451908342, 0.057980521450763045), (-0.09903371862324573, 0.03231457377154601), (-0.08007009503268847, 0.02032081957268994)}, {(0.08488216962382156, 0.005412310058084541), (0.10884638667561086, 0.008923283323243991), (0.1514145406391274, 0.017378259777899724), (0.24665640085125506, 0.04718237970828895), (0.5770211525851817, 0.3311314568812653), (-0.5770211525851846, 0.33113145688127027), (-0.24665640085125595, 0.04718237970828926), (-0.15141454063912763, 0.01737825977789978), (-0.10884638667561086, 0.008923283323244019), (-0.08488216962382156, 0.0054123100580845684)}, {(0.08388987923372415, -0.010592156468904601), (0.10676430713610774, -0.017331868041575993), (0.1458742632612966, -0.03315324165029476), (0.22359967877936116, -0.08469684802248545), (0.33476104598737516, -0.38041027953110745), (-0.33476104598737483, -0.3804102795311108), (-0.22359967877936182, -0.08469684802248595), (-0.14587426326129682, -0.03315324165029487), (-0.10676430713610774, -0.01733186804157605), (-0.08388987923372415, -0.010592156468904601)}, {(0.07747666080809212, -0.02450492870255938), (0.09402852175879461, -0.03823724789054883), (0.1158571134609776, -0.06595956118630664), (0.13454514567230103, -0.12766499617769456), (0.08426219159718717, -0.2398599885806285), (-0.08426219159718651, -0.23985998858062907), (-0.13454514567230103, -0.127664996177695), (-0.11585711346097782, -0.06595956118630686), (-0.09402852175879461, -0.03823724789054883), (-0.07747666080809212, -0.02450492870255938)}, {(0.0678370438986633, -0.034346786115358574), (0.07696337113632934, -0.05010115556114969), (0.08380337527264303, -0.07637534882802255), (0.07731120144730741, -0.1174310294710994), (0.03524281349194591, -0.16059509329852562), (-0.03524281349194558, -0.16059509329852562), (-0.07731120144730719, -0.11743102947109962), (-0.08380337527264303, -0.07637534882802255), (-0.07696337113632978, -0.05010115556114969), (-0.0678370438986633, -0.034346786115358574)}, {(0.057396464792191626, -0.03996736153143132), (0.06082430982949649, -0.05445553063468722), (0.05966823856647552, -0.07478871265775311), (0.047666399401361303, -0.09957583056761665), (0.019044794543057242, -0.11935459307381846), (-0.019044794543057075, -0.11935459307381846), (-0.047666399401361303, -0.09957583056761665), (-0.05966823856647552, -0.07478871265775311), (-0.06082430982949649, -0.05445553063468722), (-0.057396464792191626, -0.03996736153143132)}, {(0.047729245010124544, -0.042305467168064936), (0.0476692729232111, -0.05432439868846428), (0.043268978619005694, -0.06903368861486836), (0.03167999999999993, -0.08423999999999987), (0.011866993774822865, -0.09466624579460925), (-0.011866993774822754, -0.09466624579460925), (-0.03167999999999993, -0.08423999999999987), (-0.043268978619005694, -0.06903368861486836), (-0.0476692729232111, -0.05432439868846428), (-0.047729245010124544, -0.042305467168064936)}}
Textfield(Pot) → InputBox1
Plane(xAxis, yAxis) → c