Geometric Interpretation of these equations of motion?
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I was reading my Engineering Mechanics book, and it derived some strange looking integrals I'll have to apply. I could memorize them, but I'd rather understand them - then I won't have to memorize.
A few words mentioning Leibniz notion, and viola - we have these relationships:
∫vv0dv=∫t0acdt∫v0vdv=∫0tacdt
∫ss0ds=∫t0(v0+act)dt∫s0sds=∫0t(v0+act)dt
∫vv0vdv=∫ss0acds∫v0vvdv=∫s0sacds
I can manipulate them given appropriate data, but they don't really mean much to me. (I do easily understand things like a=dvdta=dvdt,however).
I anyone could point me to website that discuss or even just show me how to derive these, I would really appreciate it - I find it easier to understand geometric interpretations, but I would appreciate any knowledge you would be willing to share.
A few words mentioning Leibniz notion, and viola - we have these relationships:
∫vv0dv=∫t0acdt∫v0vdv=∫0tacdt
∫ss0ds=∫t0(v0+act)dt∫s0sds=∫0t(v0+act)dt
∫vv0vdv=∫ss0acds∫v0vvdv=∫s0sacds
I can manipulate them given appropriate data, but they don't really mean much to me. (I do easily understand things like a=dvdta=dvdt,however).
I anyone could point me to website that discuss or even just show me how to derive these, I would really appreciate it - I find it easier to understand geometric interpretations, but I would appreciate any knowledge you would be willing to share.
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Explanation:
The fundamental solutions of the Tschauner–Hempel equations, which describe the motion of a deputy satellite relative.
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