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        "quote": "The last step follows either by direct differentiation of $L = { \\textstyle { \\frac { 1 } { 2 } } } g _ { i j } \\dot { q } ^ { i } \\dot { q } ^ { j } - U ( q )$ or by applying Euler’s theorem on homogeneous functions to $T ( q ^ { j } , \\lambda \\dot { q } ^ { i } ) = \\lambda ^ { 2 } T ( q ^ { j } , \\dot { q } ^ { i } )$ ). The components $p _ { i }$ of the momentum 1-form, given by <a href=\"#equation-16-30\" class=\"cross-reference\" id=\"xref-05-classical-mechanics-10\" data-reference=\"equation-16-30\">Eq. (16.30)</a>, are called the <u class=\"concept-term\" data-concept-identity=\"urn:uuid:1d84079a-778c-4a1c-bd5d-6518d57af2b6\" data-concept-route=\"/concept-identities#concept-1d84079a-778c-4a1c-bd5d-6518d57af2b6\" id=\"first-cab1c4adb17c06967cba-en\">generalized momenta</u> conjugate to the generalized coordinates $q ^ { i }$",
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