= Lagrangian coordinate
{title2=$\mathbf q$}
A <Lagrangian coordinate> labels a material particle and follows its identity as the body moves. Taking the particle's position $\mathbf X$ in a <reference configuration> as its label gives the <deformation map> $\mathbf x=\boldsymbol\chi(\mathbf X,t)$. Differentiation at fixed $\mathbf X$ gives that particle's <velocity> and <acceleration>.
A floating marker in water approximates a <Lagrangian trajectory>, while a fixed current meter records an <Eulerian coordinate> description. The distinction is useful because a particle can cross regions with different <velocity> even when every fixed-location reading is steady. For a conserved material element, <mass conservation> becomes $\rho J=\rho_0$, relating its current <mass density> to its changing <volume>. Material labels are especially natural for <elasticity>, where the same region's initial and final lengths are compared to define <strain>.
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