some typos and index list extension, vib Ch

Author: sveinlin

doc/.src/chapters/vib/vib_app.do.txt

@@ -142,7 +142,7 @@ Finally, we have the external environmental force $\F_e = F(t)\ii$.
 Newton's second law of motion now involves three forces:
 
 !bt
-\[ F(t)\ii + f(\dot u)\ii - s(u)\ii = m\ddot u \ii\tp\]
+\[ F(t)\ii - f(\dot u)\ii - s(u)\ii = m\ddot u \ii\tp\]
 !et
 The common mathematical form of the ODE problem is
 
@@ -261,7 +261,7 @@ label{vib:app:washmach}
 
 A washing machine is placed on four springs with efficient dampers.
 If the machine contains just a few clothes, the circular motion of
-the machine induces a sinusoidal external force and the machine will
+the machine induces a sinusoidal external force from the floor and the machine will
 jump up and down if the frequency of the external force is close to
 the natural frequency of the machine and its spring-damper system.
 
@@ -274,8 +274,10 @@ label{vib:app:pendulum}
 
 === Simple pendulum ===
 
+idx{pendulum! simple}
+
 A classical problem in mechanics is the motion of a pendulum. We first
-consider a "simple pendulum" :
+consider a "simplified pendulum" :
 "https://en.wikipedia.org/wiki/Pendulum" (sometimes also called a
 mathematical pendulum): a small body of mass $m$ is
 attached to a massless wire and can oscillate back and forth in the
@@ -379,6 +381,8 @@ and carry out specific simulations with this model.
 
 === Physical pendulum ===
 
+idx{pendulum! physical}
+
 The motion of a compound or physical pendulum where the wire is a rod with
 mass, can be modeled very similarly. The governing equation is
 $I\acc = \bm{T}$ where $I$ is the moment of inertia of the entire body about
@@ -404,6 +408,8 @@ label{vib:app:pendulum:thetaeq_physical}
 ===== Dynamic free body diagram during pendulum motion =====
 label{vib:app:pendulum_bodydia}
 
+idx{free body diagram! dynamic} idx{free body diagram! animated} idx{`Pysketcher`}
+
 Usually one plots the mathematical quantities as functions of time to
 visualize the solution of ODE models.  Exercise
 ref{vib:exer:pendulum_simple} asks you to do this for the motion of a
@@ -534,6 +540,8 @@ listed below.
 ===== Motion of an elastic pendulum =====
 label{vib:app:pendulum_elastic}
 
+idx{pendulum! elastic} idx{differential-algebraic equation} idx{constrained motion}
+
 Consider a pendulum as in Figure ref{vib:app:pendulum:fig_problem}, but
 this time the wire is elastic. The length of the wire when it is not
 stretched is $L_0$, while $L(t)$ is the stretched
@@ -712,6 +720,8 @@ label{vib:app:pendulum_elastic:vy0}
 
 === Scaling ===
 
+idx{round-off error} idx{scaling}
+
 The elastic pendulum model can be used to study both an elastic pendulum
 and a classic, non-elastic pendulum. The latter problem is obtained
 by letting $k\rightarrow\infty$. Unfortunately,

doc/.src/chapters/vib/vib_gen.do.txt

@@ -17,7 +17,7 @@ mu^{\prime\prime} + f(u^{\prime}) + s(u) = F(t),\quad u(0)=I,\ u^{\prime}(0)=V,\
 label{vib:ode2}
 \end{equation}
 !et
-We have also included a possibly nonzero initial value of $u^{\prime}(0)$.
+We have also included a possibly nonzero initial value for $u^{\prime}(0)$.
 The parameters $m$, $f(u^{\prime})$, $s(u)$, $F(t)$, $I$, $V$, and $T$ are
 input data.
 
@@ -231,7 +231,7 @@ mathematics,
 label{vib:ode2:nonlin:fbdiff}
 \end{equation}
 !et
-The forward and backward differences have both an error proportional
+The forward and backward differences both have an error proportional
 to $\Delta t$ so one may think the discretization above leads to
 a first-order scheme.
 However, by looking at the formulas, we realize that the forward-backward
@@ -328,20 +328,20 @@ machine precision).
 === Catching bugs ===
 
 How good are the constant and quadratic solutions at catching
-bugs in the implementation?
+bugs in the implementation? Let us check that by introducing some bugs.
 
- * Use `m` instead of `2*m` in the denominator of `u[1]`: constant
-   works, while quadratic fails.
+ * Use `m` instead of `2*m` in the denominator of `u[1]`: code works for constant
+   solution, but fails (as it should) for a quadratic one.
  * Use `b*dt` instead of `b*dt/2` in the updating formula for `u[n+1]`
-   in case of linear damping: constant and quadratic fail.
+   in case of linear damping: constant and quadratic both fail.
  * Use `F[n+1]` instead of `F[n]` in case of linear or quadratic damping:
    constant solution works, quadratic fails.
 
-We realize that the constant solution is very useful to catch bugs because
+We realize that the constant solution is very useful for catching certain bugs because
 of its simplicity (easy to predict what the different terms in the
-formula should evaluate to), while it seems the quadratic solution is
-capable of detecting all other types of typos in the scheme (?).
-This results demonstrates why we focus so much on exact, simple polynomial
+formula should evaluate to), while the quadratic solution seems
+capable of detecting all (?) other kinds of typos in the scheme.
+These results demonstrate why we focus so much on exact, simple polynomial
 solutions of the numerical schemes in these writings.
 
 # More: classes, cases with pendulum approx u vs sin(u),
@@ -448,7 +448,7 @@ u^{\prime} &= v\tp
 label{vib:ode2:EulerCromer:ueq}
 \end{align}
 !et
-The idea is to step (ref{vib:ode2:EulerCromer:veq}) forward using
+Again, the idea is to step (ref{vib:ode2:EulerCromer:veq}) forward using
 a standard Forward Euler method, while we update $u$ from
 (ref{vib:ode2:EulerCromer:ueq}) with a Backward Euler method,
 utilizing the recent, computed $v^{n+1}$ value. In detail,
@@ -617,7 +617,7 @@ periods. Define
 !bt
 \[ g(u,v) = \frac{1}{m}(F(t)-s(u)-f(v))\tp\]
 !et
-The algorithm is explicit and features these simple steps:
+The algorithm is explicit and features these steps:
 
 !bt
 \begin{align}

doc/.src/chapters/vib/vib_undamped.do.txt

@@ -2799,15 +2799,15 @@ in operator notation as
 !bt
 \begin{align}
 \lbrack D_t u &= v\rbrack^{n+\half},\\
-\lbrack D_t v &= -\omega u\rbrack^{n+1}
+\lbrack D_t v &= -\omega^2 u\rbrack^{n+1}
 \tp
 \end{align}
 !et
 or if we switch the sequence of the equations:
 
 !bt
 \begin{align}
-\lbrack D_t v &= -\omega u\rbrack^{n},\\
+\lbrack D_t v &= -\omega^2 u\rbrack^{n},\\
 \lbrack D_t u &= v\rbrack^{n+\half}
 \tp
 \end{align}

doc/Trash/vib/html/._vib-sol000.html

@@ -7,7 +7,7 @@
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="description" content="Finite Difference Computing for Oscillatory Phenomena">
-<meta name="keywords" content="vibration ODE,oscillations,mechanical vibrations,angular frequency,period (of oscillations),frequency (of oscillations),Hz (unit),mesh finite differences,mesh function,discretization of domain,centered difference,finite differences centered,Verlet integration,Stoermer's method,Leapfrog method,FD operator notation,vectorization,test function,pytest,nose,verification hand calculations,unit testing,zeros,verification polynomial solutions,assert,verification convergence rates,error norm,slope marker (in convergence plots),SciTools,making movies,animation,WebM (video format),Ogg (video format),MP4 (video format),Flash (video format),video formats,HTML5 video tag,ImageMagic,Bokeh,sympy,error mesh function,error global,error norm,norm,stability criterion,1st-order ODE,2nd-order ODE,Odespy,phase plane plot,mechanical energy,energy principle,kinetic energy,potential energy,spring constant,stiffness,Newton's 2nd law,error norm,forward-backward scheme,Euler-Cromer scheme,semi-implicit Euler,semi-explicit Euler,symplectic scheme,verification  convergence rates,Stoermer-Verlet algorithm,staggered mesh,staggered Euler-Cromer scheme,alternating mesh,nonlinear restoring force,nonlinear spring,forced vibrations,geometric mean,averaging geometric,DOF (degree of freedom),resonance">
+<meta name="keywords" content="vibration ODE,oscillations,mechanical vibrations,angular frequency,period (of oscillations),frequency (of oscillations),Hz (unit),mesh finite differences,mesh function,discretization of domain,centered difference,finite differences centered,Verlet integration,Stoermer's method,Leapfrog method,FD operator notation,vectorization,test function,pytest,nose,verification hand calculations,unit testing,zeros,verification polynomial solutions,assert,verification convergence rates,error norm,slope marker (in convergence plots),SciTools,making movies,animation,WebM (video format),Ogg (video format),MP4 (video format),Flash (video format),video formats,HTML5 video tag,ImageMagic,Bokeh,sympy,error mesh function,error global,error norm,norm,stability criterion,1st-order ODE,2nd-order ODE,Odespy,phase plane plot,mechanical energy,energy principle,kinetic energy,potential energy,spring constant,stiffness,Newton's 2nd law,error norm,forward-backward scheme,Euler-Cromer scheme,semi-implicit Euler,semi-explicit Euler,symplectic scheme,verification  convergence rates,Stoermer-Verlet algorithm,staggered mesh,staggered Euler-Cromer scheme,alternating mesh,nonlinear restoring force,nonlinear spring,forced vibrations,geometric mean,averaging geometric,DOF (degree of freedom),pendulum  simple,pendulum  physical,free body diagram  dynamic,free body diagram  animated,pendulum  elastic,differential-algebraic equation,constrained motion,round-off error,scaling,resonance">
 
 <title>Finite Difference Computing for Oscillatory Phenomena</title>
 
@@ -662,7 +662,7 @@
 <center>[3] <b>Department of Process, Energy and Environmental Technology, University College of Southeast Norway</b></center>
 <br>
 <p>
-<center><h4>Dec 1, 2016</h4></center> <!-- date -->
+<center><h4>Dec 2, 2016</h4></center> <!-- date -->
 <br>
 <p>
 <!-- Externaldocuments: ../../../../../decay-book/doc/.src/book/book -->

doc/Trash/vib/html/._vib-sol001.html

@@ -7,7 +7,7 @@
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="description" content="Finite Difference Computing for Oscillatory Phenomena">
-<meta name="keywords" content="vibration ODE,oscillations,mechanical vibrations,angular frequency,period (of oscillations),frequency (of oscillations),Hz (unit),mesh finite differences,mesh function,discretization of domain,centered difference,finite differences centered,Verlet integration,Stoermer's method,Leapfrog method,FD operator notation,vectorization,test function,pytest,nose,verification hand calculations,unit testing,zeros,verification polynomial solutions,assert,verification convergence rates,error norm,slope marker (in convergence plots),SciTools,making movies,animation,WebM (video format),Ogg (video format),MP4 (video format),Flash (video format),video formats,HTML5 video tag,ImageMagic,Bokeh,sympy,error mesh function,error global,error norm,norm,stability criterion,1st-order ODE,2nd-order ODE,Odespy,phase plane plot,mechanical energy,energy principle,kinetic energy,potential energy,spring constant,stiffness,Newton's 2nd law,error norm,forward-backward scheme,Euler-Cromer scheme,semi-implicit Euler,semi-explicit Euler,symplectic scheme,verification  convergence rates,Stoermer-Verlet algorithm,staggered mesh,staggered Euler-Cromer scheme,alternating mesh,nonlinear restoring force,nonlinear spring,forced vibrations,geometric mean,averaging geometric,DOF (degree of freedom),resonance">
+<meta name="keywords" content="vibration ODE,oscillations,mechanical vibrations,angular frequency,period (of oscillations),frequency (of oscillations),Hz (unit),mesh finite differences,mesh function,discretization of domain,centered difference,finite differences centered,Verlet integration,Stoermer's method,Leapfrog method,FD operator notation,vectorization,test function,pytest,nose,verification hand calculations,unit testing,zeros,verification polynomial solutions,assert,verification convergence rates,error norm,slope marker (in convergence plots),SciTools,making movies,animation,WebM (video format),Ogg (video format),MP4 (video format),Flash (video format),video formats,HTML5 video tag,ImageMagic,Bokeh,sympy,error mesh function,error global,error norm,norm,stability criterion,1st-order ODE,2nd-order ODE,Odespy,phase plane plot,mechanical energy,energy principle,kinetic energy,potential energy,spring constant,stiffness,Newton's 2nd law,error norm,forward-backward scheme,Euler-Cromer scheme,semi-implicit Euler,semi-explicit Euler,symplectic scheme,verification  convergence rates,Stoermer-Verlet algorithm,staggered mesh,staggered Euler-Cromer scheme,alternating mesh,nonlinear restoring force,nonlinear spring,forced vibrations,geometric mean,averaging geometric,DOF (degree of freedom),pendulum  simple,pendulum  physical,free body diagram  dynamic,free body diagram  animated,pendulum  elastic,differential-algebraic equation,constrained motion,round-off error,scaling,resonance">
 
 <title>Finite Difference Computing for Oscillatory Phenomena</title>
 

doc/Trash/vib/html/._vib-sol002.html

@@ -7,7 +7,7 @@
 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
 <meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
 <meta name="description" content="Finite Difference Computing for Oscillatory Phenomena">
-<meta name="keywords" content="vibration ODE,oscillations,mechanical vibrations,angular frequency,period (of oscillations),frequency (of oscillations),Hz (unit),mesh finite differences,mesh function,discretization of domain,centered difference,finite differences centered,Verlet integration,Stoermer's method,Leapfrog method,FD operator notation,vectorization,test function,pytest,nose,verification hand calculations,unit testing,zeros,verification polynomial solutions,assert,verification convergence rates,error norm,slope marker (in convergence plots),SciTools,making movies,animation,WebM (video format),Ogg (video format),MP4 (video format),Flash (video format),video formats,HTML5 video tag,ImageMagic,Bokeh,sympy,error mesh function,error global,error norm,norm,stability criterion,1st-order ODE,2nd-order ODE,Odespy,phase plane plot,mechanical energy,energy principle,kinetic energy,potential energy,spring constant,stiffness,Newton's 2nd law,error norm,forward-backward scheme,Euler-Cromer scheme,semi-implicit Euler,semi-explicit Euler,symplectic scheme,verification  convergence rates,Stoermer-Verlet algorithm,staggered mesh,staggered Euler-Cromer scheme,alternating mesh,nonlinear restoring force,nonlinear spring,forced vibrations,geometric mean,averaging geometric,DOF (degree of freedom),resonance">
+<meta name="keywords" content="vibration ODE,oscillations,mechanical vibrations,angular frequency,period (of oscillations),frequency (of oscillations),Hz (unit),mesh finite differences,mesh function,discretization of domain,centered difference,finite differences centered,Verlet integration,Stoermer's method,Leapfrog method,FD operator notation,vectorization,test function,pytest,nose,verification hand calculations,unit testing,zeros,verification polynomial solutions,assert,verification convergence rates,error norm,slope marker (in convergence plots),SciTools,making movies,animation,WebM (video format),Ogg (video format),MP4 (video format),Flash (video format),video formats,HTML5 video tag,ImageMagic,Bokeh,sympy,error mesh function,error global,error norm,norm,stability criterion,1st-order ODE,2nd-order ODE,Odespy,phase plane plot,mechanical energy,energy principle,kinetic energy,potential energy,spring constant,stiffness,Newton's 2nd law,error norm,forward-backward scheme,Euler-Cromer scheme,semi-implicit Euler,semi-explicit Euler,symplectic scheme,verification  convergence rates,Stoermer-Verlet algorithm,staggered mesh,staggered Euler-Cromer scheme,alternating mesh,nonlinear restoring force,nonlinear spring,forced vibrations,geometric mean,averaging geometric,DOF (degree of freedom),pendulum  simple,pendulum  physical,free body diagram  dynamic,free body diagram  animated,pendulum  elastic,differential-algebraic equation,constrained motion,round-off error,scaling,resonance">
 
 <title>Finite Difference Computing for Oscillatory Phenomena</title>
 
@@ -3758,7 +3758,7 @@ <h2 id="vib:model2x2:staggered">The Euler-Cromer scheme on a staggered mesh</h2>
 \begin{align}
 \lbrack D_t u &= v\rbrack^{n+\half},
 \tag{63}\\ 
-\lbrack D_t v &= -\omega u\rbrack^{n+1}
+\lbrack D_t v &= -\omega^2 u\rbrack^{n+1}
 \tp
 \tag{64}
 \end{align}
@@ -3768,7 +3768,7 @@ <h2 id="vib:model2x2:staggered">The Euler-Cromer scheme on a staggered mesh</h2>
 
 $$
 \begin{align}
-\lbrack D_t v &= -\omega u\rbrack^{n},
+\lbrack D_t v &= -\omega^2 u\rbrack^{n},
 \tag{65}\\ 
 \lbrack D_t u &= v\rbrack^{n+\half}
 \tp