An Investigation Into Optimal Descent Trajectories for Multipurpose Long Range Space Vehicles Under Advanced Conditions

In this work, we investigate the problem of fuel-optimal control of space vehicle descent trajectories. The main tool we use to establish optimality is Pontryagin’s Maximum Principle. We present a variety of scenarios with increasing complexities, including drag, wind, and moving landing platforms in the context of differing atmospheric and gravitational conditions. Throughout the paper, we use a balance of analytical and numerical techniques. Finally, observations and conclusions drawn from the investigation form the basis for suggestions into additional areas of analysis

Prominence in Singapore and American English: Evidence from reading aloud

English has spread far beyond the boundaries of the traditional L1 varieties (eg British, American, Australian English). Not only is English a leading foreign language throughout the world, it is also a central language for many multilingual communities throughout the world. The speakers of these new Englishes are not yet fully seen as ‘native speakers’ by many speakers from the traditional L1 varieties but cannot be called ‘non‐native speakers’ in any meaningful sense of the word. Kachru (1990) calls these new varieties ‘outer circle’ Englishes, a contrast to the ‘inner circle’ native speaker varieties and the ‘expanding circle’ foreign language speakers of English. The outer circle varieties of English (eg Singapore, Indian, Nigerian English) differ from the inner circle varieties in a number of ways, but few are more noticeable in speech than differences in prosody, that is, in the use of stress, rhythmic structure and intonation. To those familiar only with inner circle varieties, outer circle speakers of English can sound both fluent and choppy, comfortable with English yet incomprehensible, perfectly grammatical yet far too fast. These inner circle judgements grow out of unfamiliarity with the music of outer circle speech. One area of difference between inner and outer circle Englishes is intonation, or the systematic use of voice pitch to communicate phrase‐level meaning