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typo on contact models
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docs/src/linearized_friction.md

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@@ -16,9 +16,9 @@ $$\text{minimize}_{\beta} \quad [v^T -v^T] \beta, \\
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\text{subject to} \quad \beta^T \mathbf{1} \leq \mu \gamma, \\
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\beta \geq 0,$$
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which satisfies the LCP formulation, is instead solved. Here, the friction cone is linearized (Fig. \ref{friction_cones}) and the friction vector, $\beta \in \mathbf{R}^{4}$, is correspondingly overparameterized and subject to additional non-negative constraints \cite{stewart1996implicit}.
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which satisfies the LCP formulation, is instead solved. Here, the friction cone is linearized and the friction vector, $\beta \in \mathbf{R}^{4}$, is correspondingly overparameterized and subject to additional non-negative constraints.
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The optimality conditions of \eqref{mdp_linear} and constraints used in the LCP are:
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The optimality conditions of the above problem and constraints used in the LCP are:
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$$[v^T -v^T]^T + \psi \mathbf{1} - \eta = 0, \\
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\mu \gamma -\beta^T \textbf{1} \geq 0,\\

docs/src/nonlinear_friction.md

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@@ -25,7 +25,8 @@ The second-order-cone product is:
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$$\beta \circ \eta = (\beta^T \eta, \beta_{(1)} \eta_{(2:n)} + \eta_{(1)} \beta_{(2:n)}),$$
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and,
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$$\mathbf{e} = (1, 0, \dots, 0) \label{soc_identity},$$
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$$\mathbf{e} = (1, 0, \dots, 0),$$
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is its corresponding identity element. Friction is recovered from the solution: $b = \beta^*_{(2:3)}$. The benefits of this model are increased physical fidelity and fewer optimization variables, without substantial increase in computational cost.
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