#] #] ********************* #] "$d_Qtest"'symbols flatliner derivations/symParen_file_bads test.txt' - test outpt??? # www.BillHowell.ca ?date? initial # view this file in a text editor, with [constant width font, tab = 3 spaces], no line-wrap %7) ∂[∂(t): Rpcs(POIo(t),t)] = [ - Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle) + Vons(particle)^2*t ] /[ Rocs(POIo)^2 - 2*Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle)*t + (Vons(particle) *t)^2 ]^(1/2) From "Relating [Rpcs,Rθ0pcs,RθPI2pcs,Aθpc,Aθpc]@t to [Rocs,Rθ0ocs,RθPI2ocs,Aθoc,APo] for (POIo)" : % 2) Rpcs(POIo(t),t)) = { Rocs(POIo)^2 - 2*Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle)*t + [Vons(particle) *t]^2 }^(1/2) therefore : ∂[∂(t): sin(Aθpc(POIo(t),t))] = Rocs(POIo)*sin(Aθoc(POIo)) *(-1)/Rpcs(POIo(t),t)^2 *∂[∂(t): Rpcs(POIo(t),t)] = -1*Rocs(POIo)*sin(Aθoc(POIo)) / { Rocs(POIo)^2 - 2*Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle)*t + [Vons(particle) *t]^2 }^(1/2)^2 * [ - Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle) + Vons(particle)^2*t ] /[ Rocs(POIo)^2 - 2*Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle)*t + (Vons(particle) *t)^2 ]^(1/2) = -1*Rocs(POIo)*sin(Aθoc(POIo)) / { Rocs(POIo)^2 - 2*Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle)*t + [Vons(particle) *t]^2 } * [ - Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle) + Vons(particle)^2*t ] /[ Rocs(POIo)^2 - 2*Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle)*t + (Vons(particle) *t)^2 ]^(1/2) = -1*Rocs(POIo)*sin(Aθoc(POIo))*Vons(particle) / { Rocs(POIo)^2 - 2*Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle)*t + [Vons(particle) *t]^2 } * [ - Rocs(POIo)*cos(Aθoc(POIo)) + Vons(particle) *t ] / [ Rocs(POIo)^2 - 2*Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle)*t + (Vons(particle) *t)^2 ]^(1/2) Finally : 1) ∂[∂(t): sin(Aθpc(POIo(t),t))] = -Rocs(POIo)*sin(Aθoc(POIo))*Vons(particle) * [ - Rocs(POIo)*cos(Aθoc(POIo)) + Vons(particle) *t ] / [ Rocs(POIo)^2 - 2*Rocs(POIo)*cos(Aθoc(POIo))*Vons(particle)*t + (Vons(particle) *t)^2 ]^(3/2) +-----+ Expression for dp[dt : cosAθoc(POIp(t),t)] dp[dt : cosAθoc(POIp(t),t)] = dp[dt : [ Rpcs(POIp)*cos(Aθpc(POIo(t),t)) + Vons(particle)*t ] /{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(1/2) ] = dp[dt : [Rpcs(POIp)*cos(Aθpc(POIo(t),t)) + Vons(particle)*t ] ] /{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(1/2) + [ Rpcs(POIp)*cos(Aθpc(POIo(t),t)) + Vons(particle)*t ] *dp[dt :{Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(-1/2)] = Vons(particle) /{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(1/2) + [ Rpcs(POIp)*cos(Aθpc(POIo(t),t)) + Vons(particle)*t ] *{(-1/2)/{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(3/2) *dp[dt : { Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 } } = Vons(particle) /{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(1/2) - [ Rpcs(POIp)*cos(Aθpc(POIo(t),t)) + Vons(particle)*t ] *{ /{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(3/2) * (1/2)*{ 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle) + 2*[Vons(particle)*t] *dp[dt : [Vons(particle)*t] ] } } = Vons(particle) /{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(1/2) - *[ Rpcs(POIp)*cos(Aθpc(POIo(t),t)) + Vons(particle)*t ] *{1/{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(3/2) * { Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle) + [Vons(particle)^2*t] } } = Vons(particle) / { Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(1/2) - [ Rpcs(POIp)*cos(Aθpc(POIo(t),t)) + Vons(particle)*t ] * { Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle) + [Vons(particle)^2*t] } / { Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(3/2) = Vons(particle) /{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(1/2) - *[ Rpcs(POIp)*cos(Aθpc(POIo(t),t)) + Vons(particle)*t ] *{ + Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle) + [Vons(particle)^2*t] } /{ Rpcs(POIp)^2 + 2*Rpcs(POIp)*cos(Aθpc(POIo(t),t))*Vons(particle)*t + [Vons(particle)*t]^2 }^(3/2) Subbing (4)*,(2)*,(1)* into (1) : 1) ∂[∂(t): BT_BARNpdv(POIo(t),t)] = |Q(particle)|*Vons(particle)/c *Rodh(Vonv_X_Rpcv(POIo(t),t)) *{ ∂[∂(t): f_BARNES(Vonv(particle),Aθpd(POIo(t),t))]* sin(Aθpc(POIo(t),t)) *Rpcs(POIp)^(-2) + f_BARNES(Vonv(particle),Aθpd(POIo(t),t)) *∂[∂(t): sin(Aθpc(POIo(t),t))] *Rpcs(POIp)^(-2) + f_BARNES(Vonv(particle),Aθpd(POIo(t),t)) * sin(Aθpc(POIo(t),t)) *∂[∂(t): Rpcs(POIp)^( - 2)] } = |Q(particle)|*Vons(particle)/c *Rodh(Vonv_X_Rpcv(POIo(t),t)) *{ 3*β^2/{1 - [β*sin(Aθpd(POIo(t),t))]^2} *f_BARNES(Vonv(particle),Aθpd(POIo(t),t)) *Vons(particle)*sin(Aθpc(POIo(t),t))^2*cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t) *sin(Aθpc(POIo(t),t)) *Rpcs(POIp)^(-2) + f_BARNES(Vonv(particle),Aθpd(POIo(t),t)) *Rpcs(POIp)^(-2) *Vons(particle)*sin(Aθpc(POIo(t),t)) *cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t) + f_BARNES(Vonv(particle),Aθpd(POIo(t),t)) * sin(Aθpc(POIo(t),t)) *(-2)*Rpcs(POIp)^(-3)*∂[∂(t): Rpcs(POIp)] } = |Q(particle)|*Vons(particle)/c *Rodh(Vonv_X_Rpcv(POIo(t),t)) *{ 3*β^2/{1 - [β*sin(Aθpd(POIo(t),t))]^2} *f_BARNES(Vonv(particle),Aθpd(POIo(t),t)) *Vons(particle)*sin(Aθpc(POIo(t),t))^2*cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t) *sin(Aθpc(POIo(t),t)) *Rpcs(POIp)^(-2) + f_BARNES(Vonv(particle),Aθpd(POIo(t),t)) *Rpcs(POIp)^(-2) *Vons(particle)*sin(Aθpc(POIo(t),t)) *cos(Aθpc(POIo(t),t))/Rpcs(POIo(t),t) + f_BARNES(Vonv(particle),Aθpd(POIo(t),t)) * sin(Aθpc(POIo(t),t)) *(-2)*Rpcs(POIp)^(-3) *-Vons(particle)*cos(Aθpc(POIo(t),t)) } = f_BARNES(Vonv(particle),Aθpd(POIo(t),t))*|Q(particle)|*Vons(particle)^2/c*cos(Aθpc(POIo(t),t)) *Rodh(Vonv_X_Rpcv(POIo(t),t)) *{ 3*β^2/{1 - [β*sin(Aθpd(POIo(t),t))]^2} *sin(Aθpc(POIo(t),t))^2/Rpcs(POIo(t),t) *sin(Aθpc(POIo(t),t)*Rpcs(POIp)^( - 2) + sin(Aθpc(POIo(t),t)) /Rpcs(POIo(t),t) *Rpcs(POIp)^(-2) + sin(Aθpc(POIo(t),t)) *(-2)*Rpcs(POIp)^(-3) *(-1) } = f_BARNES(Vonv(particle),Aθpd(POIo(t),t))*|Q(particle)|*Vons(particle)^2/c*cos(Aθpc(POIo(t),t)) *Rodh(Vonv_X_Rpcv(POIo(t),t)) *{ { 3*β^2/{1 - [β*sin(Aθpd(POIo(t),t))]^2} *sin(Aθpc(POIo(t),t))^3/Rpcs(POIo(t),t)^3 + sin(Aθpc(POIo(t),t)) /Rpcs(POIo(t),t)^3 + 2*sin(Aθpc(POIo(t),t)) /Rpcs(POIp)^3 } = f_BARNES(Vonv(particle),Aθpd(POIo(t),t))*|Q(particle)|*Vons(particle)^2/c*sin(Aθpc(POIo(t),t))*cos(Aθpc(POIo(t),t))/Rpcs(POIp)^3 *Rodh(Vonv_X_Rpcv(POIo(t),t)) *{ { 3*β^2/{1 - [β*sin(Aθpd(POIo(t),t))]^2} *sin(Aθpc(POIo(t),t))^2 + 1 + 2 } = 3*f_BARNES(Vonv(particle),Aθpd(POIo(t),t))*|Q(particle)|*Vons(particle)^2/c*sin(Aθpc(POIo(t),t))*cos(Aθpc(POIo(t),t))/Rpcs(POIp)^3 *{ { [β*sin(Aθpc(POIo(t),t))]^2/{1 - [β*sin(Aθpd(POIo(t),t))]^2} + 1 } *Rodh(Vonv_X_Rpcv(POIo(t),t))