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equations: Fix syntax errors in built-in equations

Browse source 
Fix various syntax errors in the built-in equations contributed by
@Wiljea.

Also some changes in units:

* use `Ω` (Unicode 937) character instead of `Ω` (Unicode 8486) for
  the Ohm unit. There is a dedicated Unicode codepoint, but since we
  don't use special characters for `m` or `s` units, there is no
  reason we should make things more difficult for Ohm.

* Use metric units consistently, i.e. replace `_lb` with `_kg`, `_in`
  with `_cm`, `_lbf` with `_N` and so on. It might be worth it later
  to make a metric and an imperial variant of this file.

* Use degrees for user angles input in equations.

* Rename variables that are reserved words, e.g. `Re` and `vx`.
  This is because DB48X is by default case-insensitive.
  Note that we could have a prefix character forcing a symbol for
  reserved names (much like we have a prefix for constants).

Fixes: #1162

Signed-off-by: Christophe de Dinechin <christophe@dinechin.org>
This commit is contained in:
Christophe de Dinechin 2024-09-03 21:15:03 +02:00
parent 9ac7a00e4f
commit 4c75e9c894
6 changed files with 130 additions and 130 deletions
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4
doc/commands/symbolic.md
View file

@ -137,7 +137,7 @@ Names are sorted in decreasing order of size, and for the same size,
in alphabetical order.
`'A*Foo*G(X;Y;cos Z)` ▶ `'A*Foo*G(X;Y;cos Z)` `[ Foo A G X Y Z ]`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `'(U_V)=(I_A)*(R_Ω)'` `[ I R U ]`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `'(U_V)=(I_A)*(R_Ω)'` `[ I R U ]`
As a DB48X extension, this command also applies to programs, list and
arrays. Another extension is the [`ExpressionVariables`](#expressionvariables)
@ -155,7 +155,7 @@ If there are units in the expression, the units are returned in the resulting
list.
`'A*Foo*G(X;Y;cos Z)` ▶ `{ Foo A G X Y Z }`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `{ (I_A) (R_Ω) (U_V) }`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `{ (I_A) (R_Ω) (U_V) }`
This is a variation of the HP command [`LNAME`](#listexpressionnames), which is
a bit more convenient to use in programs.

4
help/db48x.md
View file

@ -8962,7 +8962,7 @@ Names are sorted in decreasing order of size, and for the same size,
in alphabetical order.
`'A*Foo*G(X;Y;cos Z)` ▶ `'A*Foo*G(X;Y;cos Z)` `[ Foo A G X Y Z ]`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `'(U_V)=(I_A)*(R_Ω)'` `[ I R U ]`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `'(U_V)=(I_A)*(R_Ω)'` `[ I R U ]`
As a DB48X extension, this command also applies to programs, list and
arrays. Another extension is the [`ExpressionVariables`](#expressionvariables)
@ -8980,7 +8980,7 @@ If there are units in the expression, the units are returned in the resulting
list.
`'A*Foo*G(X;Y;cos Z)` ▶ `{ Foo A G X Y Z }`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `{ (I_A) (R_Ω) (U_V) }`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `{ (I_A) (R_Ω) (U_V) }`
This is a variation of the HP command [`LNAME`](#listexpressionnames), which is
a bit more convenient to use in programs.

4
help/db50x.md
View file

@ -8962,7 +8962,7 @@ Names are sorted in decreasing order of size, and for the same size,
in alphabetical order.
`'A*Foo*G(X;Y;cos Z)` ▶ `'A*Foo*G(X;Y;cos Z)` `[ Foo A G X Y Z ]`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `'(U_V)=(I_A)*(R_Ω)'` `[ I R U ]`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `'(U_V)=(I_A)*(R_Ω)'` `[ I R U ]`
As a DB50X extension, this command also applies to programs, list and
arrays. Another extension is the [`ExpressionVariables`](#expressionvariables)
@ -8980,7 +8980,7 @@ If there are units in the expression, the units are returned in the resulting
list.
`'A*Foo*G(X;Y;cos Z)` ▶ `{ Foo A G X Y Z }`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `{ (I_A) (R_Ω) (U_V) }`
`'(U_V)=(I_A)*(R_Ω)'` ▶ `{ (I_A) (R_Ω) (U_V) }`
This is a variation of the HP command [`LNAME`](#listexpressionnames), which is
a bit more convenient to use in programs.

2
src/characters.cc
View file

@ -250,7 +250,7 @@ static const cstring basic_characters[] =
"ềỂểỄễỆệỈỉỊịỌọỎỏỐốỒồỔổỖỗỘộỚớỜờỞởỠỡỢợỤụỦủỨứỪừỬửỮữỰựỲỳỴỵỶỷỸỹ"
"      ‐–—―‗‘’‚‛“”„†‡•…‰′″‹›‼‽‾"
"⁄ ⁰⁳⁴⁵⁶⁷⁸⁹⁻ⁿ₀₁₂₃₄₅₆₇₈₉₣₤₧₫€₭₹₺₽"
"ℂ℅ℊℎℏℓ№ℚℝ℡™ΩÅ℮ℼⅈⅉ⅛⅜⅝⅞"
"ℂ℅ℊℎℏℓ№ℚℝ℡™ΩΩÅ℮ℼⅈⅉ⅛⅜⅝⅞"
"ⅠⅡⅢⅣⅤⅥⅦⅧⅨⅩⅪⅫⅬⅭⅮⅯ"
"←↑→↓↔↕↨⇄⇆∂∆∏∑−∕∙√∛∜∞∟∠∡∩∫≈≠≡≤≥⊿⌂⌐⌠⌡"
"─│┌┐└┘├┤┬┴┼═║╒╓╔╕╖╗╘╙╚╛╜╝╞╟╠╡╢╣╤╥╦╧╨╩╪╫╬"

244
src/equations.cc
View file

@ -115,12 +115,12 @@ static const cstring basic_equations[] =
"}",
"E Field Infinite Line", "{ "
" '(E_(N/C))=1/(2*Ⓒπ*Ⓒε0*εr)*((λ_(C/m))/(r_m)' "
" '(E_(N/C))=1/(2*Ⓒπ*Ⓒε0*εr)*(λ_(C/m))/(r_m)' "
" '(λ_(C/m))=(Q_C)/(L_m)' "
"}",
"E Field Finite Line", "{ "
" '(E_(N/C))=1/(4*Ⓒπ*Ⓒε0*εr)*((λ_(C/m))/(r_m)*((SIN(θ1_r)-SIN(θ2_r))' "
" '(E_(N/C))=1/(4*Ⓒπ*Ⓒε0*εr)*(λ_(C/m))/(r_m)*(SIN(θ1_°)-SIN(θ2_°))' "
" '(λ_(C/m))=(Q_C)/(L_m)' "
"}",
@ -211,13 +211,13 @@ static const cstring basic_equations[] =
"}",
"RL Transient", "{ "
" '(I_A)=1/(R_Ω)*((Vf_V)-((Vf_V)-(Vi_V))*EXP((-(t_μs))/((R_Ω)*(L_mH)))' "
" '(I_A)=1/(R_Ω)*((Vf_V)-((Vf_V)-(Vi_V))*EXP((-(t_μs))/((R_Ω)*(L_mH))))' "
"}",
"Resonant Frequency", "{ "
" 'Qs=1/(R_Ω)*√((L_mH)/(C_μF))' "
" 'Qp=(R_Ω)*√((C_μF)/(L_mH))' "
" '(ω0_(r/s))=2*(Ⓒπ_r)*(f0_Hz) "
" '(ω0_(r/s))=2*(Ⓒπ_r)*(f0_Hz)' "
" '(ω0_(r/s))=1/√((L_mH)*(C_μF))' "
"}",
@ -253,21 +253,21 @@ static const cstring basic_equations[] =
// Example of the following in
// https://en.wikipedia.org/wiki/Drift_velocity#Numerical_example
"Drift Speed % Current Density", "{ "
"Drift Speed & Current Density", "{ "
" '(vd_(m/s))=(I_A)/((n_(m^-3))*Ⓒqe*(A_(cm^2)))' "
" '(J_(A/m^2))=(vd_(m/s))*(ρ_(C/m^3)) "
" '(J_(A/m^2))=(vd_(m/s))*(ρ_(C/m^3))' "
" '(J_(A/m^2))=(σ_(S/m))*(E_(V_m))' "
"}",
// Example of the following in
// https://en.wikipedia.org/wiki/Electron_mobility#Examples
"Electron % Hole Mobilities", "{ "
"Electron & Hole Mobilities", "{ "
" '(J_(A/m^2))=(Je_(A/m^2))+(Jh_(A/m^2))' "
" '(Je_(A/m^2))=Ⓒqe*(ne_(m^-3))*(μe_(cm^2/(V*s)))*(E_(V/m)) "
" '(Jh_(A/m^2))=Ⓒqe*(nh_(m^-3))*(μh_(cm^2/(V*s)))*(E_(V/m)) "
" '(Je_(A/m^2))=Ⓒqe*(ne_(m^-3))*(μe_(cm^2/(V*s)))*(E_(V/m))' "
" '(Jh_(A/m^2))=Ⓒqe*(nh_(m^-3))*(μh_(cm^2/(V*s)))*(E_(V/m))' "
" '(μe_(cm^2/(V*s)))=Ⓒqe*(τc_s)/(meeff_kg)' "
" '(μh_(cm^2/(V*s)))=Ⓒqe*(τc_s)/(mheff_kg)' "
" '(σ_(S/m)=Ⓒqe*((μe_(cm^2/(V*s)))*(ne_(m^-3))+(μh_(cm^2/(V*s)))*(nh_(m^-3)))' "
" '(σ_(S/m))=Ⓒqe*((μe_(cm^2/(V*s)))*(ne_(m^-3))+(μh_(cm^2/(V*s)))*(nh_(m^-3)))' "
"}",
// ------------------------------------------------------------------------
@ -322,8 +322,8 @@ static const cstring basic_equations[] =
" '(M_(kg/s))=(ρ_(kg/m^3))*(Q_(m^3/s))' "
" '(Q_(m^3/s))=(A_(m^2))*(vavg_(m/s))' "
" '(A_(m^2))=Ⓒπ*(D_m)^2/4' "
" 'Re=(D_m)*(vavg_(m/s))*((ρ_(kg/m^3))*(μ_(kg/(m*s)))' "
" '(n_((m^2)/s))=(μ_(kg/(m*s)))/(ρ_(kg/m^3))' "
" 'Reynolds=(D_m)*(vavg_(m/s))*(ρ_(kg/m^3))*(μ_(kg/(m*s)))' "
" '(n_(m^2/s))=(μ_(kg/(m*s)))/(ρ_(kg/m^3))' "
"}",
// ------------------------------------------------------------------------
@ -405,8 +405,8 @@ static const cstring basic_equations[] =
"}",
"Polytropic Processes", "{ "
"'(Pf_psi)/(Pi_psi)=((Vf_(ft^3))/(Vi_(ft^3)))^(-n)' "
"'(Tf_°F)/(Ti_°F)=((Pf_psi)/(Pi_psi))^((n-1)/n)' "
"'(Pf_atm)/(Pi_atm)=((Vf_(ft^3))/(Vi_(ft^3)))^(-n)' "
"'(Tf_°F)/(Ti_°F)=((Pf_atm)/(Pi_atm))^((n-1)/n)' "
"}",
"Isentropic Flow", "{ "
@ -437,8 +437,8 @@ static const cstring basic_equations[] =
// ------------------------------------------------------------------------
// 17 eqns
"Heat Capacity", "{ "
"'(Q_kJ))=(m_kg)*(c_(kJ/(kg*K)))*(ΔT_°C)' "
"'(Q_kJ))=(m_kg)*(c_(kJ/(kg*K)))*((Tf_°C)-(Ti_°C))' "
"'(Q_kJ)=(m_kg)*(c_(kJ/(kg*K)))*(ΔT_°C)' "
"'(Q_kJ)=(m_kg)*(c_(kJ/(kg*K)))*((Tf_°C)-(Ti_°C))' "
"}",
"Thermal Expansion", "{ "
@ -453,7 +453,7 @@ static const cstring basic_equations[] =
"Convection", "{ "
"'(q_W)=(h_(W/(m^2*K)))*(A_(m^2))*(ΔT_°C)' "
"'(q_W)=(h_(W/(m^2*K)))*(A_(m^2))(Th_°C)-(Tc_°C)' "
"'(q_W)=(h_(W/(m^2*K)))*(A_(m^2))*((Th_°C)-(Tc_°C))' "
"}",
"Conduction + Convection", "{ "
@ -480,47 +480,47 @@ static const cstring basic_equations[] =
// WARNING both HP50G & HP50G_AUR.pdf used a variables rw absent from all
// equations
"Straight Wire Infinite", "{ "
"'(B_T)=Ⓒμ0*Ⓒμr*(I_A)/(2*Ⓒπ*(r_cm))' "
"'(B_T)=Ⓒμ0*μr*(I_A)/(2*Ⓒπ*(r_cm))' "
"}",
"Straight Wire Finite", "{ "
"'(B_T)=Ⓒμ0*Ⓒμr*(I_A)/(a*Ⓒπ*(r_m))*(COS(θ1_r)-COS(θ2_r))' "
"'(B_T)=Ⓒμ0*μr*(I_A)/(a*Ⓒπ*(r_m))*(COS(θ1_°)-COS(θ2_°))' "
"}",
"Force Between Wires", "{ "
"'(Fba_N)=(Ⓒμ0*Ⓒμr*(Ib_A)*(Ia_A)*(L_cm))/(2*Ⓒπ*(d_m))' "
"'(Fba_N)=(Ⓒμ0*μr*(Ib_A)*(Ia_A)*(L_cm))/(2*Ⓒπ*(d_m))' "
"}",
"B Field In Infinite Solenoid", "{ "
"'(B_T)=Ⓒμ0*Ⓒμr*(I_A)*n' "
"'(B_T)=Ⓒμ0*μr*(I_A)*n' "
"}",
"B Field In Finite Solenoid", "{ "
"'(B_T)=(1/2)*Ⓒμ0*Ⓒμr*(I_A)*n*(COS(α2_r)-COS(α1_r))' "
"'(B_T)=(1/2)*Ⓒμ0*μr*(I_A)*n*(COS(α2_°)-COS(α1_°))' "
"}",
"B Field In Toroid", "{ "
"'(B_T)=(Ⓒμ0*Ⓒμr*(I_A)*N)/(2*Ⓒπ)*(2/((ro_cm)+(ri_cm)))' "
"'(B_T)=(Ⓒμ0*μr*(I_A)*N)/(2*Ⓒπ)*(2/((ro_cm)+(ri_cm)))' "
"}",
"Hall Effect", "{ "
"'(VH_V)=((I_A)*(B_T))/((n_(1/m^3))*ABS(q_C))*(l_m))' "
"'(VH_V)=((I_A)*(B_T))/((n_(1/m^3))*ABS(q_C))*(l_m)' "
"}",
"Cyclotron Mouvement", "{ "
"'(Rc_m)=((m_kg)*(v_(m/s)))/(ABS(q_C))*(B_T))' "
"'(Rc_m)=((m_kg)*(v_(m/s)))/(ABS(q_C)*(B_T))' "
"'(fc_Hz)=(ABS(q_C)*(B_T))/(2*Ⓒπ*(m_kg))' "
"'(T_s)=1/(fc_Hz)' "
"}",
"Helicoidal Mouvement", "{ "
"'(Rc_m)=((m_kg)*(v_(m/s))*SIN(θ_°))/(ABS(q_C))*(B_T))' "
"'(Rc_m)=((m_kg)*(v_(m/s))*SIN(θ_°))/(ABS(q_C)*(B_T))' "
"'(T_s)=(2*Ⓒπ*(Rc_m))/((v_(m/s))*SIN(θ_°))' "
"'(Dpitch_m)=(v_(m/s))*COS(θ_°)*(T_s)' "
"}",
"Volumic Density Magnetic Energy", "{ "
"'(uB_(J/m^3))=(1/(2*Ⓒμ0*Ⓒμr))*(B_T)^2' "
"'(uB_(J/m^3))=(1/(2*Ⓒμ0*μr))*(B_T)^2' "
"}",
// ------------------------------------------------------------------------
@ -535,39 +535,39 @@ static const cstring basic_equations[] =
"}",
"Object In Free Fall", "{ "
"'(y_ft)=(y0_ft)+(v0_(ft/s))*(t_s)-1/2*Ⓒg*(t_s)^2' "
"'(y_ft)=(y0_ft)+(v_(ft/s))*(t_s)+1/2*Ⓒg*(t_s)^2' "
"'(v_(ft/s))=(v0_(ft/s))-Ⓒg*(t_s)' "
"'(v_(ft/s))^2=(v0_(ft/s))^2-2*Ⓒg*((y_ft)-(y0_ft))' "
"'(y_m)=(y0_m)+(v0_(m/s))*(t_s)-1/2*Ⓒg*(t_s)^2' "
"'(y_m)=(y0_m)+(v_(m/s))*(t_s)+1/2*Ⓒg*(t_s)^2' "
"'(v_(m/s))=(v0_(m/s))-Ⓒg*(t_s)' "
"'(v_(m/s))^2=(v0_(m/s))^2-2*Ⓒg*((y_m)-(y0_m))' "
"}",
"Projectile Motion", "{ "
"'(x_ft)=(x0_ft)+(v0_(ft/s))*COS(θ0_°)*(t_s)' "
"'(y_ft)=(y0_ft)+(v0_(ft/s))*SIN(θ0_°)*(t_s)-1/2*Ⓒg*(t_s)^2' "
"'(vx_(ft/s))=(v0_(ft/s))*COS(θ0_r)' "
"'(vy_(ft/s))=(v0_(ft/s))*SIN(θ0_r)-Ⓒg*(t_s)' "
"'(R_m)=((v0_(m/s))^2)/Ⓒg*SIN(2*(θ0_r))' "
"'(x_m)=(x0_m)+(v0_(m/s))*COS(θ0_°)*(t_s)' "
"'(y_m)=(y0_m)+(v0_(m/s))*SIN(θ0_°)*(t_s)-1/2*Ⓒg*(t_s)^2' "
"'(v0x_(m/s))=(v0_(m/s))*COS(θ0_°)' "
"'(v0y_(m/s))=(v0_(m/s))*SIN(θ0_°)-Ⓒg*(t_s)' "
"'(R_m)=((v0_(m/s))^2)/Ⓒg*SIN(2*(θ0_°))' "
"}",
"Angular Motion", "{ "
"'(θ_°)=(θ0_°)+(ω0_(r/min))*(t_s)+1/2*(α_(r/min^2))*(t_s)^2' "
"'(θ_°)=(θ0_°)+(ω_(r/min))*(t_s)-1/2*(α_(r/min^2))*(t_s)^2' "
"'(θ_°)=(θ0_°)+1/2*((ω0_(r/min))+(ω_(r/min)))*(t_s)' "
"'(ω_(r/min))=(ω0_(r/min))+(α_(r/min^2))*(t_s)' "
"'(θ_°)=(θ0_°)+(ω0_rpm)*(t_s)+1/2*(α_(rpm^2))*(t_s)^2' "
"'(θ_°)=(θ0_°)+(ω_rpm)*(t_s)-1/2*(α_(rpm^2))*(t_s)^2' "
"'(θ_°)=(θ0_°)+1/2*((ω0_rpm)+(ω_rpm))*(t_s)' "
"'(ω_rpm)=(ω0_rpm)+(α_(rpm^2))*(t_s)' "
"}",
"Circular Motion", "{ "
"'(ω_(r/min))=(v_(ft/s))/(r_in)' "
"'(ar_(ft/s^2))=(v_(ft/s))^2/(r_in)' "
"'(ω_(r/min))=2*(Ⓒπ_r)*(N_(rpm))' "
"'(ω_rpm)=(v_(m/s))/(r_cm)' "
"'(ar_(m/s^2))=(v_(m/s))^2/(r_cm)' "
"'(ω_rpm)=2*(Ⓒπ_r)*(N_rpm)' "
"}",
"Terminal Velocity", "{ "
"'(v_(ft/s))=√((2*(m_lb)*Ⓒg)/(Cd*(ρ_(lb/ft^3))*(A_in^2)))' "
"'(v_(m/s))=√((2*(m_kg)*Ⓒg)/(Cd*(ρ_(lb/ft^3))*(A_cm^2)))' "
"}",
"Escape Velocity", "{ "
"'(v_(ft/s))=√((2*ⒸG*(M_lb))/(R_mi))' "
"'(v_(m/s))=√((2*ⒸG*(M_kg))/(R_mi))' "
"}",
@ -619,21 +619,21 @@ static const cstring basic_equations[] =
"}",
"Malus Law", "{ "
"'I_(W/m^2)/I0_(W/m^2)=(COS(θ_r))^2' "
"'I0_(W/m^2)=(1/(2*Ⓒμ0*Ⓒc))*(E0_(V/m))^2' "
"'(I_(W/m^2))/(I0_(W/m^2))=(COS(θ_°))^2' "
"'(I0_(W/m^2))=(1/(2*Ⓒμ0*Ⓒc))*(E0_(V/m))^2' "
"}",
"2 Slits Young Interference", "{ "
"'I_(W/m^2)/Imax_(W/m^2)=4*(COS(Δφ_r)/2)^2' "
"'(Δφ_r)=(2*Ⓒπ*(d_μm)*SIN(θ_r))/(λ_nm)' "
"'TAN(θ_r)=(y_m)/(L_m)' "
"'(I_(W/m^2))/(Imax_(W/m^2))=4*(COS(Δφ_°)/2)^2' "
"'(Δφ_°)=(2*Ⓒπ*(d_μm)*SIN(θ_°))/(λ_nm)' "
"'TAN(θ_°)=(y_m)/(L_m)' "
"'(Δyint_m)=(λ_nm)*(L_m)/(d_μm)' "
"}",
"One Slit Diffraction", "{ "
"'I_(W/m^2)/Imax_(W/m^2)=(IFTE(α_r;SIN(α)/α;1))^2' "
"'(α_r)=(Ⓒπ*(a_μm)*SIN(θ_r))/(λ_nm)' "
"'TAN(θ_r)=(y_m)/(L_m)' "
"'(I_(W/m^2))/(Imax_(W/m^2))=(IFTE(α_°;SIN(α)/α;1))^2' "
"'(α_°)=(Ⓒπ*(a_μm)*SIN(θ_°))/(λ_nm)' "
"'TAN(θ_°)=(y_m)/(L_m)' "
"'(Δydiff_m)=2*(λ_nm)*(L_m)/(a_μm)' "
"}",
@ -661,17 +661,17 @@ static const cstring basic_equations[] =
"}",
"Torsional Pendulum", "{ "
"'(ω_(r/s))=√(((G_kPa)*(J_(mm^4)))/((L_cm)*(I_(kg*m^2))))' "
"'(ω_(r/s))=√(((G_kPa)*(J_(cm^4)))/((L_cm)*(I_(kg*m^2))))' "
"'(T_s)=2*(Ⓒπ_r)/(ω_(r/s))' "
"'(ω_(r/s))=2*(Ⓒπ_r)*(f_Hz)' "
"}",
"Simple Harmonic", "{ "
"'(x_cm)=(xm_cm)*COS((ω0_(r/s))*(t_s)+(φ_°))' "
"'(v_(m/s))=-(ω0_(r/s))*(xm_m)*SIN((ω0_(r/s))*(t_s)+(φ_r))' "
"'(a_(m/s^2))=-(ω0_(r/s))^2*(xm_m)*COS((ω0_(r/s))*(t_s)+(φ_r))' "
"'(v_(m/s))=-(ω0_(r/s))*(xm_m)*SIN((ω0_(r/s))*(t_s)+(φ_°))' "
"'(a_(m/s^2))=-(ω0_(r/s))^2*(xm_m)*COS((ω0_(r/s))*(t_s)+(φ_°))' "
"'(ω0_(r/s))=√((k_(N/m))/(m_kg))' "
"'(E_J)=(!/2)*(m_kg)*((ω0_(r/s))*(xm_m))^2' "
"'(E_J)=(1/2)*(m_kg)*((ω0_(r/s))*(xm_m))^2' "
"}",
// Ref.: https://scholar.harvard.edu/files/david-morin/files/waves_oscillations.pdf
"Underdamped Oscillations", "{ "
@ -681,7 +681,7 @@ static const cstring basic_equations[] =
"'(ωu_(r/s))=(ω0_(r/s))*√(1-((γ_(r/s))/(2*(ω0_(r/s))))^2)' "
"'(v_(m/s))=(xm_m)*EXP(-(γ_(r/s))*(t_s)/2)*(-((γ_(r/s))/2)*COS((ωu_(r/s))*(t_s)+(φ_°))-(ωu_(r/s))*SIN((ωu_(r/s))*(t_s)+(φ_°)))' "
"'(a_(m^2/s))=-((ω0_(r/s))^2*(x_m)+(γ_(r/s))*(v_m/s))' "
"'(E_J)=(!/2)*(k_(N/m))*(x_m))^2+(1/2)*(m_kg)*(v_(m/s))^2' "
"'(E_J)=(1/2)*(k_(N/m))*(x_m)^2+(1/2)*(m_kg)*(v_(m/s))^2' "
"'Q=(ω0_(r/s))/(γ_(r/s))' "
"}",
// Ref.: https://scholar.harvard.edu/files/david-morin/files/waves_oscillations.pdf
@ -694,7 +694,7 @@ static const cstring basic_equations[] =
"'TAN(φ_°)=-((γ_(r/s))*(ω_(r/s)))/((ω0_(r/s))^2-(ω_(r/s))^2)' "
"'(v_(m/s))=-(xp_m)*(ω_(r/s))*SIN((ω_(r/s))*(t_s)+(φ_°))+(xh_m)*EXP(-(γ_(r/s))*(t_s)/2)*(-((γ_(r/s))/2)*COS((ωh_(r/s))*(t_s)+(θ_°))-(ωh_(r/s))*SIN((ωh_(r/s))*(t_s)+(θ_°)))' "
"'(a_(m^2/s))=-((ω0_(r/s))^2*(x_m)+(γ_(r/s))*(v_m/s))+((Fd_N)/(m_kg))*COS((ω_(r/s))*(t_s))' "
"'(E_J)=(!/2)*(k_(N/m))*(x_m))^2+(1/2)*(m_kg)*(v_(m/s))^2' "
"'(E_J)=(1/2)*(k_(N/m))*(x_m)^2+(1/2)*(m_kg)*(v_(m/s))^2' "
"'Q=(ω0_(r/s))/(γ_(r/s))' "
"}",
@ -705,50 +705,50 @@ static const cstring basic_equations[] =
"Circle", "{ "
"'(A_(cm^2))=Ⓒπ*(r_cm)^2' "
"'(C_cm)=2*Ⓒπ*(r_cm)' "
"'(I_(mm^4))=1/4*Ⓒπ*(r_cm)^4' "
"'(J_(mm^4))=1/2*Ⓒπ*(r_cm)^4' "
"'(Id_(mm^4))=(I_(mm^4))+(A_(cm^2))*(d_cm)^2' "
"'(I_(cm^4))=1/4*Ⓒπ*(r_cm)^4' "
"'(J_(cm^4))=1/2*Ⓒπ*(r_cm)^4' "
"'(Id_(cm^4))=(I_(cm^4))+(A_(cm^2))*(d_cm)^2' "
"}",
"Ellipse", "{ "
"'(A_(m^2))=Ⓒπ*(b_μm)*(h_μin)' "
"'(C_m)=2*Ⓒπ*√(((b_μm)^2+(h_μin)^2)/2)' "
"'(I_(mm^4))=1/4*Ⓒπ*(b_μm)*(h_μin)^3' "
"'(J_(mm^4))=1/4*Ⓒπ*(b_μm)*(h_μm)*((b_μin)^2+(h_μin)^2)' "
"'(Id_(mm^4))=(I_(mm^4)+(A_(cm^2))*(d_ft)^2' "
"'(A_(cm^2))=Ⓒπ*(b_cm)*(h_cm)' "
"'(C_cm)=2*Ⓒπ*√(((b_cm)^2+(h_cm)^2)/2)' "
"'(I_(cm^4))=1/4*Ⓒπ*(b_cm)*(h_cm)^3' "
"'(J_(cm^4))=1/4*Ⓒπ*(b_cm)*(h_cm)*((b_cm)^2+(h_cm)^2)' "
"'(Id_(cm^4))=(I_(cm^4))+(A_(cm^2))*(d_cm)^2' "
"}",
"Rectangle", "{ "
"'(A_(m^2))=(b_chain)*(h_rd)' "
"'(P_cm)=2*((b_chain)+(h_rd))' "
"'(I_(m^4))=1/12*(b_chain)*(h_rd)^3' "
"'(J_(km^4))=1/12*(b_chain)*(h_rd)*((b_chain)^2+(h_rd)^2)' "
"'(Id_(km^4))=(I_(km^4))+(A_(cm^2))*(d_in)^2' "
"'(A_(cm^2))=(b_cm)*(h_cm)' "
"'(P_cm)=2*((b_cm)+(h_cm))' "
"'(I_(m^4))=1/12*(b_cm)*(h_cm)^3' "
"'(J_(cm^4))=1/12*(b_cm)*(h_cm)*((b_cm)^2+(h_cm)^2)' "
"'(Id_(cm^4))=(I_(cm^4))+(A_(cm^2))*(d_cm)^2' "
"}",
"Regular Polygon", "{ "
"'(A_(m^2))=(1/4*n*(L_yd)^2)/TAN((180_°)/n)' "
"'(P_cm)=n*(L_yd)' "
"'(rs_cm)=((L_yd)/2)/TAN((180_°)/n)' "
"'(rv_cm)=((L_yd)/2)/SIN((180_°)/n)' "
"'(A_(cm^2))=(1/4*n*(L_yd)^2)/TAN((180_°)/n)' "
"'(P_cm)=n*(L_cm)' "
"'(rs_cm)=((L_cm)/2)/TAN((180_°)/n)' "
"'(rv_cm)=((L_cm)/2)/SIN((180_°)/n)' "
"'(θ_°)=(n-2)/n*(180_°)' "
"'(β_°)=(360_°)/n' "
"}",
"Circular Ring", "{ "
"'(A_(cm^2))=Ⓒπ*((ro_μ)^2-(ri_Å)^2)' "
"'(I_(mm^4))=Ⓒπ/4*((ro_μ)^4-(ri_Å)^4)' "
"'(J_(mm^4))=Ⓒπ/2*((ro_μ)^4-(ri_Å)^4)' "
"'(Id_(mm^4))=(I_(m^4))+(A_(m^2))*(d_m)^2' "
"'(A_(cm^2))=Ⓒπ*((ro_cm)^2-(ri_cm)^2)' "
"'(I_(cm^4))=Ⓒπ/4*((ro_cm)^4-(ri_cm)^4)' "
"'(J_(cm^4))=Ⓒπ/2*((ro_cm)^4-(ri_cm)^4)' "
"'(Id_(cm^4))=(I_(m^4))+(A_(m^2))*(d_cm)^2' "
"}",
"Triangle", "{ "
"'(A_(in^2))=(b_in)*(h_in)/2' "
"'(P_in)=(b_in)+√((v_in)^2+(h_in)^2)+√(((b_in)-(v_in))^2+(h_in)^2)' "
"'(Ix_(in^4))=1/36*(b_in)*(h_in)^3' "
"'(Iy_(in^4))=1/36*(b_in)*(h_in)*((b_in)^2+(v_in)^2-(b_in)*(v_in))' "
"'(J_(in^4))=1/36*(b_in)*(h_in)*((b_in)^2+(v_in)^2+(h_in)^2-(b_in)*(v_in))' "
"'(Id_(in^4))=(I_(in^4))+(A_(in^2))*(d_in)^2' "
"'(A_(in^2))=(b_cm)*(h_cm)/2' "
"'(P_cm)=(b_cm)+√((v_cm)^2+(h_cm)^2)+√(((b_cm)-(v_cm))^2+(h_cm)^2)' "
"'(Ix_(cm^4))=1/36*(b_cm)*(h_cm)^3' "
"'(Iy_(cm^4))=1/36*(b_cm)*(h_cm)*((b_cm)^2+(v_cm)^2-(b_cm)*(v_cm))' "
"'(J_(cm^4))=1/36*(b_cm)*(h_cm)*((b_cm)^2+(v_cm)^2+(h_cm)^2-(b_cm)*(v_cm))' "
"'(Id_(cm^4))=(I_(cm^4))+(A_(in^2))*(d_cm)^2' "
"}",
// ------------------------------------------------------------------------
@ -766,25 +766,25 @@ static const cstring basic_equations[] =
//WARNING mass units in the example of HP50G_AUR (12.2) is lbs...
// is it lbf or lb (lb probably)
"Cylinder", "{ "
"'(V_(in^3))=Ⓒπ*(r_in)^2*(h_in)' "
"'(A_(in^2))=2*Ⓒπ*(r_in)^2+2*Ⓒπ*(r_in)*(h_in)' "
"'(Ixx_(lb*in^2))=(1/4)*(m_lb)*(r_in)^2+(1/12)*(m_lb)*(h_in)^2' "
"'(Izz_(lb*in^2))=(1/2)*(m_lb)*(r_in)^2' "
"'(Id_(lb*m^2))=(Ixx_(kg*m^2))+(m_lb)*(d_m)^2')' "
"'(V_(cm^3))=Ⓒπ*(r_cm)^2*(h_cm)' "
"'(A_(cm^2))=2*Ⓒπ*(r_cm)^2+2*Ⓒπ*(r_cm)*(h_cm)' "
"'(Ixx_(kg*cm^2))=(1/4)*(m_kg)*(r_cm)^2+(1/12)*(m_kg)*(h_cm)^2' "
"'(Izz_(kg*cm^2))=(1/2)*(m_kg)*(r_cm)^2' "
"'(Id_(kg*m^2))=(Ixx_(kg*m^2))+(m_kg)*(d_m)^2' "
"}",
"Parallelepiped", "{ "
"'(V_(in^3))=(b_in)*(h_in)*(t_in)' "
"'(A_(in^2))=2*((b_in)*(h_in)+(b_m)*(t_in)+(h_in)*(t_in))' "
"'(I_(lb*in^2))=(1/12)*(m_lb)*((h_in)^2+(t_in)^2)' "
"'(Id_(lb*in^2))=(I_(lb*in^2))+(m_lb)*(d_in)^2')' "
"'(V_(cm^3))=(b_cm)*(h_cm)*(t_cm)' "
"'(A_(cm^2))=2*((b_cm)*(h_cm)+(b_m)*(t_cm)+(h_cm)*(t_cm))' "
"'(I_(kg*cm^2))=(1/12)*(m_kg)*((h_cm)^2+(t_cm)^2)' "
"'(Id_(kg*cm^2))=(I_(kg*cm^2))+(m_kg)*(d_cm)^2' "
"}",
"Sphere", "{ "
"'(V_(cm^3))=(4/3)*Ⓒπ*(r_cm)^3' "
"'(A_(cm^2))=4*Ⓒπ*(r_cm)^2' "
"'(I_(kg*m^2))=(2/5)*(m_kg)*(r_cm)^2' "
"'(Id_(lb*in^2))=(I_(kg*m^2))+(m_kg)*(d_cm)^2')' "
"'(Id_(kg*cm^2))=(I_(kg*m^2))+(m_kg)*(d_cm)^2' "
"}",
// ------------------------------------------------------------------------
@ -796,7 +796,7 @@ static const cstring basic_equations[] =
// ERROR in gm formula in HP50G_AUR.pdf: μm=μn (OK)
// ERROR in 4th formula of HP50G_AUR.pdf αR=>αF
"PN Step Junctions", "{ "
"'(Vbi_V)=(Ⓒk*(T_°C))/Ⓒqe*LN(((NA_(cm^-3))*(ND_(cm^-3)))/(ni^2)' "
"'(Vbi_V)=(Ⓒk*(T_°C))/Ⓒqe*LN((NA_(cm^-3))*(ND_(cm^-3)))/(ni^2)' "
"'(xd_μ)=√((2*Ⓒεsi*Ⓒε0)/Ⓒqe*((Vbi_V)-(Va_V))*(1/(NA_(cm^-3))+1/(ND_(cm^-3))))' "
"'(Cj_(pF/cm^2))=(Ⓒεsi*Ⓒε0)/(xd_μ)' "
"'(Emax_(V/m))=2*((Vbi_V)-(Va_V))/(xd_μ)' "
@ -811,13 +811,13 @@ static const cstring basic_equations[] =
"NMOS Transistor", "{ "
"'(We_μ)=(W_μ)-2*(ΔW_μ)' "
"'(Le_μ)=(L_m)-2*(ΔL_μ)' "
"'(Cox_(pF/cm^2))=(Ⓒεox*Ⓒε0)/(tox_Å)' "
"'(Cox_(pF/cm^2))=(Ⓒεox*Ⓒε0)/(tox_nm)' "
"'(IDS_mA)=(Cox_(pF/cm^2))*(μn_((cm^2)/(V*s)))*((We_μ)/(Le_μ))*(((VGS_V)-(Vt_V))*(VDS_V)-(VDS_V)^2/2)*(1+(λ_(1/V))*(VDS_V))' "
"'(γ_(V^0.5))=√((2*Ⓒεsi*Ⓒε0)*Ⓒqe*(NA_(cm^-3)))/(Cox_(pF/cm^2))' "
"'(Vt_V)=(Vt0_V)+(γ_(V^0.5))*(√(2*ABS(φp_V)-ABS(VBS_V))-√(2*ABS(φp_V)))' "
"'(γ_(V^(1/2)))=√((2*Ⓒεsi*Ⓒε0)*Ⓒqe*(NA_(cm^-3)))/(Cox_(pF/cm^2))' "
"'(Vt_V)=(Vt0_V)+(γ_(V^(1/2)))*(√(2*ABS(φp_V)-ABS(VBS_V))-√(2*ABS(φp_V)))' "
"'(φp_V)=Ⓒk*(T_K)/Ⓒqe*LN((NA_(cm^-3))/ni)' "
"'(gds_S)=(IDS_mA)*(λ_(V^-1))' "
"'(gm_(mA/V))=√((Cox_(pF/cm^2))*(μn_((cm^2)/(V*s)))*((We_m)/(Le_m))*(1+(λ_(V^-1)*(VDS_V)))*2*(IDS_mA))' "
"'(gm_(mA/V))=√((Cox_(pF/cm^2))*(μn_((cm^2)/(V*s)))*((We_m)/(Le_m))*(1+(λ_(V^-1))*(VDS_V))*2*(IDS_mA))' "
"'(VDsat_V)=(VGS_V)-(Vt_V)' "
"}",
@ -840,7 +840,7 @@ static const cstring basic_equations[] =
"'(Vbi_V)=(Ⓒk*(T_K))/Ⓒqe*LN((ND_(cm^-3))/ni)' "
"'(xdmax_μ)=√((2*Ⓒεsi*Ⓒε0)/(Ⓒqe*(ND_(cm^-3)))*((Vbi_V)-(VGS_V)+(VDS_V)))' "
"'(G0_S)=Ⓒqe*(ND_(cm^-3))*(μn_((cm^2)/(V*s)))*(((a_μ)*(W_μ))/(L_μ))' "
"'(ID_mA)=(G0_S)*((VDS_V)-((2/3)*√((2*Ⓒεsi*Ⓒε0)/(*Ⓒqe*(ND_(cm^-3))*(a_μ)^2)))*(((Vbi_V)-(VGS_V)+(VDS_V))^(3/2)-((Vbi_V)-(VGS_V))^(3/2)))' "
"'(ID_mA)=(G0_S)*((VDS_V)-((2/3)*√((2*Ⓒεsi*Ⓒε0)/(Ⓒqe*(ND_(cm^-3))*(a_μ)^2)))*(((Vbi_V)-(VGS_V)+(VDS_V))^(3/2)-((Vbi_V)-(VGS_V))^(3/2)))' "
"'(VDsat_V)=(Ⓒqe*(ND_(cm^-3))*(a_μ)^2)/(2*Ⓒεsi*Ⓒε0)-((Vbi_V)-(VGS_V))' "
"'(Vt_V)=(Vbi_V)-(Ⓒqe*(ND_(cm^-3))*(a_μ)^2)/(2*Ⓒεsi*Ⓒε0)' "
"'(gm_(mA/V))=(G0_S)*(1-√(((2*Ⓒεsi*Ⓒε0)/(Ⓒqe*(ND_(cm^-3))*(a_μ)^2))*((Vbi_V)-(VGS_V))))' "
@ -851,33 +851,33 @@ static const cstring basic_equations[] =
// ------------------------------------------------------------------------
//16 eqns
"Normal Stress", "{ "
"'(σ_psi)=(E_psi)*ε' "
"'ε=(δ_in)/(L_ft)' "
"'(σ_Pa)=(P_lbf)/(A_in^2)' "
"'(σ_atm)=(E_atm)*ε' "
"'ε=(δ_cm)/(L_m)' "
"'(σ_Pa)=(P_N)/(A_cm^2)' "
"}",
"Shear Stress", "{ "
"'(τ_psi)=(G_psi)*(γ_°)' "
"'(γ_°)=((r_in)*(φ_°))/(L_ft)' "
"'(τ_psi)=((T_(ft*lbf))*(r_in))/(J_(in^4))' "
"'(τ_atm)=(G_atm)*(γ_°)' "
"'(γ_°)=((r_cm)*(φ_°))/(L_m)' "
"'(τ_atm)=((T_(cm*N))*(r_cm))/(J_(cm^4))' "
"}",
"Stress On An Element", "{ "
"'(σx1_kPa)=((σx_kPa)+(σy_kPa))/2+((σx_kPa)-(σy_kPa))/2*COS(2*(θ_°))+(τxy_kPa)*SIN(2*(θ_°))' "
"'(σx1_kPa)+(σy1_kPa)=(σx_kPa)+(σy_kPa)' "
"'(τx1y1_kPa)=-(((σx_kPa)-(σy_kPa))/2*)*SIN(2*(θ_°))+(τxy_kPa)*(σy_kPa)' "
"'(τx1y1_kPa)=-(((σx_kPa)-(σy_kPa))/2)*SIN(2*(θ_°))+(τxy_kPa)*(σy_kPa)' "
"}",
// WARNING Error in formula 1 of HP50G_AUR square missing HP50G takes
// precedence
"Mohr's Circle", "{ "
"'(σ1_psi)=((σx_psi)+(σy_psi))/2+√((((σx_psi)-(σy_psi))^2)/2+(τxy_psi)^2)' "
"'(σ1_psi)+(σ2_psi)=(σx_psi)+(σy_psi)' "
"'SIN(2*(θp1_°))=(τxy_psi)/√((((σx_psi)-(σy_psi))/2)^2+(τxy_psi)^2)' "
"'(σ1_atm)=((σx_atm)+(σy_atm))/2+√((((σx_atm)-(σy_atm))^2)/2+(τxy_atm)^2)' "
"'(σ1_atm)+(σ2_atm)=(σx_atm)+(σy_atm)' "
"'SIN(2*(θp1_°))=(τxy_atm)/√((((σx_atm)-(σy_atm))/2)^2+(τxy_atm)^2)' "
"'(θp2_°)=(θp1_°)+(90_°)' "
"'(τmax_psi)=((σ1_psi)-(σ2_psi))/2' "
"'(τmax_atm)=((σ1_atm)-(σ2_atm))/2' "
"'(θs_°)=(θp1_°)-(45_°)' "
"'(σavg_psi)=((σx_psi)+(σy_psi))/2' "
"'(σavg_atm)=((σx_atm)+(σy_atm))/2' "
"}",
// ------------------------------------------------------------------------
@ -911,33 +911,33 @@ static const cstring basic_equations[] =
"Doppler Effect", "{ "
"'(f_Hz)=(f0_Hz)*(((cair_(m/s))+(vr_(m/s)))/((cair_(m/s))-(vs_(m/s))))' "
"'(cair_(m/s))=√(1.4*((8,314462618153_(J/(mol*K)))/(0.0289645_(kg/mol))*(T_K)))' "
"'(cair_(m/s))=√(1.4*((8.314462618153_(J/(mol*K)))/(0.0289645_(kg/mol))*(T_K)))' "
"}",
"Mach Number", "{ "
"'M=(u_(m/s))/(cair_(m/s))' "
"'SIN(θcone_°)=(cair_(m/s))/(u_(m/s))' "
"'(cair_(m/s))=√(1.4*((8,314462618153_(J/(mol*K)))/(0.0289645_(kg/mol))*(T_K)))' "
"'(cair_(m/s))=√(1.4*((8.314462618153_(J/(mol*K)))/(0.0289645_(kg/mol))*(T_K)))' "
"}",
"Standing Waves Cord", "{ "
"'(y_m)=(ym_m)*SIN((k_(r/m))*(x_m))*COS(ω_(r/s))*(t_s))' "
"'(y_m)=(ym_m)*SIN((k_(r/m))*(x_m))*COS((ω_(r/s))*(t_s))' "
"'(v_(m/s))=(λ_m)*(f_Hz)' "
"'(k_(r/m))=2*(Ⓒπ_r)/(λ_m)' "
"'(ω_(r/s))=2*(Ⓒπ_r)*(f_Hz)' "
"'(v_(m/s)))=√((T_N)/(ρ_(kg/m)))' "
"'(v_(m/s))=√((T_N)/(ρ_(kg/m)))' "
"'(ffixed-fixed_Hz)=(ninteger*(v_(m/s)))/(2*(L_m))' "
"'(ffixed-free_Hz)=(nodd*(v_(m/s)))/(4*(L_m))' "
"}",
"Sound Wave Harmonics", "{ "
"'(s_m)=(sm_m)*SIN((k_(r/m))*(x_m))*COS(ω_(r/s))*(t_s))' "
"'(s_m)=(sm_m)*SIN((k_(r/m))*(x_m))*COS((ω_(r/s))*(t_s))' "
"'(cair_(m/s))=(λ_m)*(f_Hz)' "
"'(k_(r/m))=2*(Ⓒπ_r)/(λ_m)' "
"'(ω_(r/s))=2*(Ⓒπ_r)*(f_Hz)' "
"'(cair_(m/s))=√(1.4*((8,314462618153_(J/(mol*K)))/(0.0289645_(kg/mol))(T_K))' "
"'(fopen-open_Hz)=(ninteger*(v_(m/s)))/(2*(L_m))' "
"'(fopen-close_Hz)=(nodd*(v_(m/s)))/(4*(L_m))' "
"'(cair_(m/s))=√(1.4*((8.314462618153_(J/(mol*K)))/(0.0289645_(kg/mol))*(T_K)))' "
"'(fopenopen_Hz)=(ninteger*(v_(m/s)))/(2*(L_m))' "
"'(fopenclose_Hz)=(nodd*(v_(m/s)))/(4*(L_m))' "
"}",
"Beat Acoustics", "{ "

2
src/unit.cc
View file

@ -665,7 +665,7 @@ static const cstring basic_units[] =
"A", "1_A", // Ampere
"V", "1_kg*m^2/(A*s^3)", // Volt
"C", "1_A*s", // Coulomb
"Ω", "1_V/A", // Ohm
"Ω", "1_V/A", // Ohm
"F", "1_C/V", // Farad
"Fdy", "96487_A*s", // Faraday