Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jacobi Fields in Optimal Control I: Morse and Maslov Indices   In this paper we discuss a general framework based on symplectic geometry for
the study of second order conditions in constrained variational problems on
curves. Using the notion of L-derivatives we construct Jacobi curves, which
represent a generalization of Jacobi fields from the classical calculus of
variations, but which also works for non-smooth extremals. This construction
includes in particular the previously known constructions for specific types of
extremals. We state and prove Morse-type theorems that connect the negative
inertia index of the Hessian of the problem to some symplectic invariants of
Jacobi curves.

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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys