# Second-Order Time-Dependent Tangent Bundles and Geometric Mechanics

Second-Order Time-Dependent Tangent Bundles and Geometric Mechanics The aim of this paper is to geometrize time-dependent Lagrangian mechanics in a way that the framework of second-order tangent bundles plays an essential role. To this end, we first introduce the concepts of time-dependent connections and time-dependent semisprays on a manifold M and their induced vector bundle structures on the second-order time-dependent tangent bundle $$\mathbb {R}\times T^2M$$ R × T 2 M . Then we turn our attention to regular time-dependent Lagrangians and their interaction with $$\mathbb {R}\times T^2M$$ R × T 2 M in different situations such as mechanical systems with potential fields, external forces and holonomic constraints. Finally, we propose some examples to support our theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

# Second-Order Time-Dependent Tangent Bundles and Geometric Mechanics

, Volume 14 (4) – Jun 23, 2017
21 pages

/lp/springer_journal/second-order-time-dependent-tangent-bundles-and-geometric-mechanics-M7XO9cQ0yF
Publisher
Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-017-0954-2
Publisher site
See Article on Publisher Site

### Abstract

The aim of this paper is to geometrize time-dependent Lagrangian mechanics in a way that the framework of second-order tangent bundles plays an essential role. To this end, we first introduce the concepts of time-dependent connections and time-dependent semisprays on a manifold M and their induced vector bundle structures on the second-order time-dependent tangent bundle $$\mathbb {R}\times T^2M$$ R × T 2 M . Then we turn our attention to regular time-dependent Lagrangians and their interaction with $$\mathbb {R}\times T^2M$$ R × T 2 M in different situations such as mechanical systems with potential fields, external forces and holonomic constraints. Finally, we propose some examples to support our theory.

### Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Jun 23, 2017

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations