Output results

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Thomas Dehaeze 2021-02-05 16:18:57 +01:00
parent 192841352e
commit e77d747590
3 changed files with 460 additions and 301 deletions

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@ -1595,7 +1595,7 @@ Usefulness of Jacobians:
\[ \dot{\mathcal{X}}_{\{M\}} = J_{\{M\}} \dot{\mathcal{L}} \] \[ \dot{\mathcal{X}}_{\{M\}} = J_{\{M\}} \dot{\mathcal{L}} \]
- $J_{\{M\}}^T$ converts $\tau$ to $\mathcal{F}_{\{M\}}$: - $J_{\{M\}}^T$ converts $\tau$ to $\mathcal{F}_{\{M\}}$:
\[ \mathcal{F}_{\{M\}} = J_{\{M\}}^T \tau \] \[ \mathcal{F}_{\{M\}} = J_{\{M\}}^T \tau \]
- $J_{\{K\}}$ converts $\dot{\mathcal{K}}$to $\dot{\mathcal{X}}_{\{K\}}$: - $J_{\{K\}}$ converts $\dot{\mathcal{K}}$ to $\dot{\mathcal{X}}_{\{K\}}$:
\[ \dot{\mathcal{X}}_{\{K\}} = J_{\{K\}} \dot{\mathcal{K}} \] \[ \dot{\mathcal{X}}_{\{K\}} = J_{\{K\}} \dot{\mathcal{K}} \]
- $J_{\{K\}}^T$ converts $\tau$ to $\mathcal{F}_{\{K\}}$: - $J_{\{K\}}^T$ converts $\tau$ to $\mathcal{F}_{\{K\}}$:
\[ \mathcal{F}_{\{K\}} = J_{\{K\}}^T \tau \] \[ \mathcal{F}_{\{K\}} = J_{\{K\}}^T \tau \]
@ -2045,7 +2045,7 @@ bi = [[-1;0.5],[-2;-1],[0;-1]]; % Joint's positions in frame {M}
#+end_src #+end_src
Let's first verify that condition eqref:eq:diag_cond_2D_1 is true: Let's first verify that condition eqref:eq:diag_cond_2D_1 is true:
#+begin_src matlab :results value replace #+begin_src matlab :results value replace :exports results
ki.*si*si' ki.*si*si'
#+end_src #+end_src
@ -2058,7 +2058,7 @@ Now, compute ${}^MO_K$:
Ok = inv([sum(ki.*si(2,:).*si, 2), -sum(ki.*si(1,:).*si, 2)])*sum(ki.*(bi(1,:).*si(2,:) - bi(2,:).*si(1,:)).*si, 2); Ok = inv([sum(ki.*si(2,:).*si, 2), -sum(ki.*si(1,:).*si, 2)])*sum(ki.*(bi(1,:).*si(2,:) - bi(2,:).*si(1,:)).*si, 2);
#+end_src #+end_src
#+begin_src matlab :results value replace :exports none :tangle no #+begin_src matlab :results value replace :exports results :tangle no
ans = Ok ans = Ok
#+end_src #+end_src
@ -2076,7 +2076,7 @@ In order to verify that the new frame $\{K\}$ indeed yields a diagonal stiffness
Jk = [si', (Kbi(1,:).*si(2,:) - Kbi(2,:).*si(1,:))']; Jk = [si', (Kbi(1,:).*si(2,:) - Kbi(2,:).*si(1,:))'];
#+end_src #+end_src
#+begin_src matlab :results value replace :exports none :tangle no #+begin_src matlab :results value replace :exports results :tangle no
ans = Jk ans = Jk
#+end_src #+end_src
@ -2090,7 +2090,7 @@ And the stiffness matrix:
K = Jk'*diag(ki)*Jk K = Jk'*diag(ki)*Jk
#+end_src #+end_src
#+begin_src matlab :results value replace :exports none :tangle no #+begin_src matlab :results value replace :exports results :tangle no
ans = K ans = K
#+end_src #+end_src
@ -2126,7 +2126,7 @@ bi = [[-L/2;h],[-L/2;-h],[L/2;h],[L/2;h]];
#+end_src #+end_src
Let's first verify that condition eqref:eq:diag_cond_2D_1 is true: Let's first verify that condition eqref:eq:diag_cond_2D_1 is true:
#+begin_src matlab :results value replace #+begin_src matlab :results value replace :exports both
ki.*si*si' ki.*si*si'
#+end_src #+end_src
@ -2139,7 +2139,7 @@ Now, compute ${}^MO_K$:
Ok = inv([sum(ki.*si(2,:).*si, 2), -sum(ki.*si(1,:).*si, 2)])*sum(ki.*(bi(1,:).*si(2,:) - bi(2,:).*si(1,:)).*si, 2); Ok = inv([sum(ki.*si(2,:).*si, 2), -sum(ki.*si(1,:).*si, 2)])*sum(ki.*(bi(1,:).*si(2,:) - bi(2,:).*si(1,:)).*si, 2);
#+end_src #+end_src
#+begin_src matlab :results value replace :exports none :tangle no #+begin_src matlab :results value replace :exports results :tangle no
ans = Ok ans = Ok
#+end_src #+end_src
@ -2157,7 +2157,7 @@ In order to verify that the new frame $\{K\}$ indeed yields a diagonal stiffness
Jk = [si', (Kbi(1,:).*si(2,:) - Kbi(2,:).*si(1,:))']; Jk = [si', (Kbi(1,:).*si(2,:) - Kbi(2,:).*si(1,:))'];
#+end_src #+end_src
#+begin_src matlab :results value replace :exports none :tangle no #+begin_src matlab :results value replace :exports results :tangle no
ans = Jk ans = Jk
#+end_src #+end_src
@ -2172,7 +2172,7 @@ And the stiffness matrix:
K = Jk'*diag(ki)*Jk K = Jk'*diag(ki)*Jk
#+end_src #+end_src
#+begin_src matlab :results value replace :exports none :tangle no #+begin_src matlab :results value replace :exports results :tangle no
ans = K ans = K
#+end_src #+end_src
@ -2353,7 +2353,7 @@ bi = [[1;-1;1],[1;1;-1],[1;1;1],[1;-1;-1],[1;-1;-1],[-1;1;-1],[1;1;-1],[-1;-1;-1
#+end_src #+end_src
Cond 1: Cond 1:
#+begin_src matlab :results value replace #+begin_src matlab :results value replace :exports both
ki.*si*si' ki.*si*si'
#+end_src #+end_src
@ -2374,7 +2374,7 @@ else
end end
#+end_src #+end_src
#+begin_src matlab :exports results :results value replace #+begin_src matlab :results value replace :exports results :tangle no
ans = Ok ans = Ok
#+end_src #+end_src

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