phases : sequence of str
The names of the phases in this trajectory to be sequentially linked.
vars : sequence of str
- The variables in the phases to be linked, or '*'. Providing '*' will time and all
+ The variables in the phases to be linked, or '*'. Providing '*' will link time and all
states. Linking control values or rates requires them to be listed explicitly.
locs : tuple of str
A two-element tuple of a location specification. For every pair in
diff --git a/api/trajectory_api.html b/api/trajectory_api.html
index 3563c01ef..a1b4c04f3 100644
--- a/api/trajectory_api.html
+++ b/api/trajectory_api.html
@@ -699,7 +699,7 @@ link_phases
- phasessequence of str
The names of the phases in this trajectory to be sequentially linked.
- varssequence of str
The variables in the phases to be linked, or ‘*’. Providing ‘*’ will time and all
+
- varssequence of str
The variables in the phases to be linked, or ‘*’. Providing ‘*’ will link time and all
states. Linking control values or rates requires them to be listed explicitly.
- locstuple of str
A two-element tuple of a location specification. For every pair in
diff --git a/contributing/contributing.html b/contributing/contributing.html
index 78bbe399d..31c58cfb5 100644
--- a/contributing/contributing.html
+++ b/contributing/contributing.html
@@ -731,21 +731,21 @@
Notebook Creation#
Both sets of equations of motion have common aerodynamic models.
First, the lift coefficient is computed using a model which assumes linearity in lift wrt the angle of attack.
-
-(21)#\[\begin{align}
+
+(21)#\[\begin{align}
C_L &= C_{L0} + \frac{\alpha}{\alpha_{max}} \left(C_{L-max} - C_{L0}\right)
\end{align}\]
Next, the drag-due-to-lift factor is computed (Equations 12.48 and 12.61 in Raymer[@raymer2012aircraft]).
-
-(22)#\[\begin{align}
+
+(22)#\[\begin{align}
K_{nom} &= \frac{1}{ \pi AR e} \\
b &= \frac{span}{2} \\
K &= 33 K_{nom} \frac{ \left(\frac{h + h_w}{b} \right) ^{\frac{3}{2}}}{1.0 + 33 \left( \frac{h + h_w}{b}\right) ^{\frac{3}{2}}}
@@ -592,8 +592,8 @@ The Aerodynamic Model
Finally, the lift and drag are computed after computing the dynamic pressure.
-
-(23)#\[\begin{align}
+
+(23)#\[\begin{align}
q &= 0.5 \rho v^2 \\
L &= q S C_L \\
D &= q S \left( C_{D0} + K C_{L}^2 \right)
@@ -604,8 +604,8 @@ Stall Speed\(\frac{v}{v_{stall}}\)).
This constraint is used to trigger the beginning of rotation and is used as a boundary constraint at the end of the initial climb.
Stall speed is given by Equation 5.6 in Raymer[@raymer2012aircraft].
-
-(24)#\[\begin{align}
+
+(24)#\[\begin{align}
W &= m g \\
v_{stall} &= \sqrt{\frac{2 * W}{\rho S C_{L-max}}}
\end{align}\]
@@ -613,8 +613,8 @@ Stall Speed
Runway Equations of Motion#
The runway equations of motion are used to integrate range and speed as the vehicle rolls along the runway.
-
-(25)#\[\begin{align}
+
+(25)#\[\begin{align}
F_r &= mg - L \cos \alpha - T \sin \alpha \\
\dot{v} &= \frac{T \cos \alpha - D - F_r \mu_r}{m} \\
\dot{r} &= v
@@ -641,8 +641,8 @@ Runway Equations of Motion
Flight Equations of Motion#
The flight equations of motion include two additional state variables: the flight-path angle (\(\gamma\)) and altitude (\(h\)).
-
-(26)#\[\begin{align}
+
+(26)#\[\begin{align}
\dot{v} &= \frac{T}{m} \cos \alpha - \frac{D}{m} - g \sin \gamma \\
\dot{\gamma} &= \frac{T}{m v} \sin \alpha + \frac{L}{m v} - \frac{g \cos \gamma}{v} \\
\dot{h} &= v \sin \gamma \\
@@ -1166,7 +1166,7 @@ Building and running the problem
-<dymos.phase.phase.Phase at 0x7f97acc620e0>
+<dymos.phase.phase.Phase at 0x7fb5f82aa7a0>
@@ -1318,9 +1318,8 @@ Building and running the problemINFO: checking out_of_order
+
+INFO: checking out_of_order
INFO:check_config:checking out_of_order
@@ -1436,19 +1435,20 @@ Building and running the problemColoring for 'traj.phases.rto.rhs_all' (class BalancedFieldODEComp)
-Coloring for 'traj.phases.rto.rhs_all' (class BalancedFieldODEComp)
-
-Jacobian shape: (132, 60) ( 9.75% nonzero)
+Jacobian shape: (132, 60) ( 9.79% nonzero)
FWD solves: 16 REV solves: 0
Total colors vs. total size: 16 vs 60 (73.3% improvement)
Sparsity computed using tolerance: 1e-25
-Time to compute sparsity: 0.023926 sec.
-Time to compute coloring: 0.016634 sec.
+Time to compute sparsity: 0.021794 sec.
+Time to compute coloring: 0.015750 sec.
Memory to compute coloring: 0.000000 MB.
Coloring for 'traj.phases.v1_to_vr.rhs_all' (class BalancedFieldODEComp)
@@ -1458,8 +1458,8 @@ Building and running the problemFull total jacobian was computed 3 times, taking 1.739460 seconds.
+Full total jacobian was computed 3 times, taking 1.337170 seconds.
Total jacobian shape: (178, 166)
@@ -1495,8 +1495,8 @@ Building and running the problem/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/recorders/sqlite_recorder.py:227: UserWarning:The existing case recorder file, dymos_solution.db, is being overwritten.
-
-
INFO: checking out_of_order
-INFO:check_config:checking out_of_order
+/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/recorders/sqlite_recorder.py:227: UserWarning:The existing case recorder file, dymos_solution.db, is being overwritten.
+INFO:check_config:checking out_of_order
INFO: checking system
@@ -995,13 +993,13 @@ Building and running the problemColoring for 'traj.phases.br_to_v1.rhs_all' (class ExplicitFuncComp)
-Jacobian shape: (132, 60) ( 9.80% nonzero)
+Jacobian shape: (132, 60) ( 9.79% nonzero)
FWD solves: 16 REV solves: 0
Total colors vs. total size: 16 vs 60 (73.3% improvement)
Sparsity computed using tolerance: 1e-25
-Time to compute sparsity: 0.406976 sec.
-Time to compute coloring: 0.084706 sec.
+Time to compute sparsity: 0.342058 sec.
+Time to compute coloring: 0.071479 sec.
Memory to compute coloring: 0.000000 MB.
@@ -1015,8 +1013,8 @@ Building and running the problemFull total jacobian was computed 3 times, taking 5.597947 seconds.
+Full total jacobian was computed 3 times, taking 4.653730 seconds.
Total jacobian shape: (178, 166)
@@ -1074,9 +1072,9 @@ Building and running the problem/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/total_jac.py:1782: DerivativesWarning:Constraints or objectives [('traj.phases.climb.timeseries.timeseries_comp.gam', inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
diff --git a/examples/brachistochrone/brachistochrone.html b/examples/brachistochrone/brachistochrone.html
index b326416f3..d98ab7d7c 100644
--- a/examples/brachistochrone/brachistochrone.html
+++ b/examples/brachistochrone/brachistochrone.html
@@ -538,8 +538,8 @@ State variables
System dynamics#
From the free-body diagram above, the evolution of the state variables is given by the following ordinary differential equations (ODE).
-
-(13)#\[\begin{align}
+
+(13)#\[\begin{align}
\frac{d x}{d t} &= v \sin(\theta) \\
\frac{d y}{d t} &= -v \cos(\theta) \\
\frac{d v}{d t} &= g \cos(\theta)
@@ -557,8 +557,8 @@ The initial and final conditions
-(14)#\[\begin{align}
+
+(14)#\[\begin{align}
x_0 &= 0 \\
y_0 &= 10 \\
v_0 &= 0
@@ -566,8 +566,8 @@ The initial and final conditions
-(15)#\[\begin{align}
+
+(15)#\[\begin{align}
x_f &= 10 \\
y_f &= 5 \\
v_f &= \mathrm{free}
@@ -733,27 +733,27 @@ Testing the ODEModel viewer data has already been recorded for Driver.
-Full total jacobian was computed 3 times, taking 0.035055 seconds.
+
@@ -1017,7 +1017,7 @@ Solving the problem with Legendre-Gauss-Lobatto collocation in Dymos/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/recorders/sqlite_recorder.py:227: UserWarning:The existing case recorder file, dymos_solution.db, is being overwritten.
-Full total jacobian was computed 3 times, taking 0.019930 seconds.
+Full total jacobian was computed 3 times, taking 0.015673 seconds.
Total jacobian shape: (12, 51)
@@ -1026,10 +1026,10 @@ Solving the problem with Legendre-Gauss-Lobatto collocation in DymosSolving the problem with Legendre-Gauss-Lobatto collocation in Dymos
@@ -1056,11 +1056,11 @@ Solving the problem with Legendre-Gauss-Lobatto collocation in Dymos
-/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/visualization/opt_report/opt_report.py:634: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
- ax.set_ylim([ymin_plot, ymax_plot])
+[1.80185208]
-[1.80185208]
+/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/visualization/opt_report/opt_report.py:634: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
+ ax.set_ylim([ymin_plot, ymax_plot])
diff --git a/examples/brachistochrone/brachistochrone_tandem_phases.html b/examples/brachistochrone/brachistochrone_tandem_phases.html
index f96ffbb47..c26ec498a 100644
--- a/examples/brachistochrone/brachistochrone_tandem_phases.html
+++ b/examples/brachistochrone/brachistochrone_tandem_phases.html
@@ -683,7 +683,7 @@ Setup and runModel viewer data has already been recorded for Driver.
-Full total jacobian was computed 3 times, taking 0.331437 seconds.
+Full total jacobian was computed 3 times, taking 0.266956 seconds.
Total jacobian shape: (223, 287)
@@ -692,8 +692,8 @@ Setup and run#
-
+